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distance. If instead of the goal being to minimize the total distance traveled to visit each desired destination but rather to minimize the total time needed to reach each destination, this goes beyond conventional optimization since travel time is inherently uncertain (traffic jams, time of day, etc.). As a result, to determine the optimal path a different simulation is required: optimization to first understand the range of potential times it could take to go from one point to another (represented by a probability distribution in this case rather than a specific distance) and then optimize the travel decisions to identify the best path to follow taking that uncertainty into account.
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a lot of time trying to estimate them by pure combinatorial calculations, I wondered whether a more practical method than "abstract thinking" might not be to lay it out say one hundred times and simply observe and count the number of successful plays. This was already possible to envisage with the beginning of the new era of fast computers, and I immediately thought of problems of neutron diffusion and other questions of mathematical physics, and more generally how to change processes described by certain differential equations into an equivalent form interpretable as a succession of random operations. Later , I described the idea to
29:
374:). In other instances, a flow of probability distributions with an increasing level of sampling complexity arise (path spaces models with an increasing time horizon, BoltzmannâGibbs measures associated with decreasing temperature parameters, and many others). These models can also be seen as the evolution of the law of the random states of a nonlinear Markov chain. A natural way to simulate these sophisticated nonlinear Markov processes is to sample multiple copies of the process, replacing in the evolution equation the unknown distributions of the random states by the sampled
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1400:. In 1946, nuclear weapons physicists at Los Alamos were investigating neutron diffusion in the core of a nuclear weapon. Despite having most of the necessary data, such as the average distance a neutron would travel in a substance before it collided with an atomic nucleus and how much energy the neutron was likely to give off following a collision, the Los Alamos physicists were unable to solve the problem using conventional, deterministic mathematical methods. Ulam proposed using random experiments. He recounts his inspiration as follows:
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this field was
Genshiro Kitagawa's, on a related "Monte Carlo filter", and the ones by Pierre Del Moral and Himilcon Carvalho, Pierre Del Moral, AndrĂ© Monin and GĂ©rard Salut on particle filters published in the mid-1990s. Particle filters were also developed in signal processing in 1989â1992 by P. Del Moral, J. C. Noyer, G. Rigal, and G. Salut in the LAAS-CNRS in a series of restricted and classified research reports with STCAN (Service Technique des Constructions et Armes Navales), the IT company DIGILOG, and the
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2271:, when planning a wireless network, the design must be proven to work for a wide variety of scenarios that depend mainly on the number of users, their locations and the services they want to use. Monte Carlo methods are typically used to generate these users and their states. The network performance is then evaluated and, if results are not satisfactory, the network design goes through an optimization process.
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2642:. However, there were many variables in play that could not be estimated perfectly, including the effectiveness of restraining orders, the success rate of petitioners both with and without advocacy, and many others. The study ran trials that varied these variables to come up with an overall estimate of the success level of the proposed program as a whole.
1605:, a Monte Carlo method, and a Monte Carlo simulation: a simulation is a fictitious representation of reality, a Monte Carlo method is a technique that can be used to solve a mathematical or statistical problem, and a Monte Carlo simulation uses repeated sampling to obtain the statistical properties of some phenomenon (or behavior).
2618:, where simulations aggregate estimates for worst-case, best-case, and most likely durations for each task to determine outcomes for the overall project. Monte Carlo methods are also used in option pricing, default risk analysis. Additionally, they can be used to estimate the financial impact of medical interventions.
2654:
in
Malaysia. The Monte Carlo simulation utilized previous published National Book publication data and book's price according to book genre in the local market. The Monte Carlo results were used to determine what kind of book genre that Malaysians are fond of and was used to compare book publications
2603:
Monte Carlo simulation is commonly used to evaluate the risk and uncertainty that would affect the outcome of different decision options. Monte Carlo simulation allows the business risk analyst to incorporate the total effects of uncertainty in variables like sales volume, commodity and labor prices,
1404:
The first thoughts and attempts I made to practice were suggested by a question which occurred to me in 1946 as I was convalescing from an illness and playing solitaires. The question was what are the chances that a
Canfield solitaire laid out with 52 cards will come out successfully? After spending
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From 1950 to 1996, all the publications on
Sequential Monte Carlo methodologies, including the pruning and resample Monte Carlo methods introduced in computational physics and molecular chemistry, present natural and heuristic-like algorithms applied to different situations without a single proof of
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algorithm in
Bayesian statistical inference. The authors named their algorithm 'the bootstrap filter', and demonstrated that compared to other filtering methods, their bootstrap algorithm does not require any assumption about that state-space or the noise of the system. Another pioneering article in
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for each variable to produce hundreds or thousands of possible outcomes. The results are analyzed to get probabilities of different outcomes occurring. For example, a comparison of a spreadsheet cost construction model run using traditional "what if" scenarios, and then running the comparison again
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The main idea behind this method is that the results are computed based on repeated random sampling and statistical analysis. The Monte Carlo simulation is, in fact, random experimentations, in the case that, the results of these experiments are not well known. Monte Carlo simulations are typically
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who developed in 1948 a mean-field particle interpretation of neutron-chain reactions, but the first heuristic-like and genetic type particle algorithm (a.k.a. Resampled or
Reconfiguration Monte Carlo methods) for estimating ground state energies of quantum systems (in reduced matrix models) is due
1345:
Despite its conceptual and algorithmic simplicity, the computational cost associated with a Monte Carlo simulation can be staggeringly high. In general the method requires many samples to get a good approximation, which may incur an arbitrarily large total runtime if the processing time of a single
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algorithms work well in a small number of dimensions, but encounter two problems when the functions have many variables. First, the number of function evaluations needed increases rapidly with the number of dimensions. For example, if 10 evaluations provide adequate accuracy in one dimension, then
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Kalos and
Whitlock point out that such distinctions are not always easy to maintain. For example, the emission of radiation from atoms is a natural stochastic process. It can be simulated directly, or its average behavior can be described by stochastic equations that can themselves be solved using
84:
Monte Carlo methods are widely used in various fields of science, engineering, and mathematics, such as physics, chemistry, biology, statistics, artificial intelligence, finance, and cryptography. They have also been applied to social sciences, such as sociology, psychology, and political science.
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is what is called a conventional optimization problem. That is, all the facts (distances between each destination point) needed to determine the optimal path to follow are known with certainty and the goal is to run through the possible travel choices to come up with the one with the lowest total
1744:
There are ways of using probabilities that are definitely not Monte Carlo simulations â for example, deterministic modeling using single-point estimates. Each uncertain variable within a model is assigned a "best guess" estimate. Scenarios (such as best, worst, or most likely case) for each input
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Branching type particle methodologies with varying population sizes were also developed in the end of the 1990s by Dan Crisan, Jessica Gaines and Terry Lyons, and by Dan Crisan, Pierre Del Moral and Terry Lyons. Further developments in this field were described in 1999 to 2001 by P. Del Moral, A.
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particles, individuals, walkers, agents, creatures, or phenotypes) interacts with the empirical measures of the process. When the size of the system tends to infinity, these random empirical measures converge to the deterministic distribution of the random states of the nonlinear Markov chain, so
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Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant
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is based on a specified subset of all permutations (which entails potentially enormous housekeeping of which permutations have been considered). The Monte Carlo approach is based on a specified number of randomly drawn permutations (exchanging a minor loss in precision if a permutation is drawn
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information with new information obtained by measuring some observable parameters (data). As, in the general case, the theory linking data with model parameters is nonlinear, the posterior probability in the model space may not be easy to describe (it may be multimodal, some moments may not be
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operations. Each simulation can generate as many as ten thousand data points that are randomly distributed based upon provided variables. Search patterns are then generated based upon extrapolations of these data in order to optimize the probability of containment (POC) and the probability of
211:
In this procedure the domain of inputs is the square that circumscribes the quadrant. One can generate random inputs by scattering grains over the square then perform a computation on each input (test whether it falls within the quadrant). Aggregating the results yields our final result, the
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P. Del Moral, G. Rigal, and G. Salut. "Estimation and nonlinear optimal control: Particle resolution in filtering and estimation". Studies on: Filtering, optimal control, and maximum likelihood estimation. Convention DRET no. 89.34.553.00.470.75.01. Research report no.4 (210p.), January
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pseudo-random uniform variable from the interval can be used to simulate the tossing of a coin: If the value is less than or equal to 0.50 designate the outcome as heads, but if the value is greater than 0.50 designate the outcome as tails. This is a simulation, but not a Monte Carlo
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in statistics, involves sampling the points randomly, but more frequently where the integrand is large. To do this precisely one would have to already know the integral, but one can approximate the integral by an integral of a similar function or use adaptive routines such as
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Before the Monte Carlo method was developed, simulations tested a previously understood deterministic problem, and statistical sampling was used to estimate uncertainties in the simulations. Monte Carlo simulations invert this approach, solving deterministic problems using
2696:) and observing that fraction of the numbers that obeys some property or properties. The method is useful for obtaining numerical solutions to problems too complicated to solve analytically. The most common application of the Monte Carlo method is Monte Carlo integration.
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and to analyze and display the models in such a way that information on the relative likelihoods of model properties is conveyed to the spectator. This can be accomplished by means of an efficient Monte Carlo method, even in cases where no explicit formula for the
2369:, occasionally referred to as Monte Carlo ray tracing, renders a 3D scene by randomly tracing samples of possible light paths. Repeated sampling of any given pixel will eventually cause the average of the samples to converge on the correct solution of the
1563:(the Laboratory for Analysis and Architecture of Systems) on radar/sonar and GPS signal processing problems. These Sequential Monte Carlo methodologies can be interpreted as an acceptance-rejection sampler equipped with an interacting recycling mechanism.
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In other problems, the objective is generating draws from a sequence of probability distributions satisfying a nonlinear evolution equation. These flows of probability distributions can always be interpreted as the distributions of the random states of a
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their consistency, nor a discussion on the bias of the estimates and on genealogical and ancestral tree based algorithms. The mathematical foundations and the first rigorous analysis of these particle algorithms were written by Pierre Del Moral in 1996.
88:
Monte Carlo methods also have some limitations and challenges, such as the trade-off between accuracy and computational cost, the curse of dimensionality, the reliability of random number generators, and the verification and validation of the results.
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P. Del Moral, G. Rigal, and G. Salut. "Nonlinear and non
Gaussian particle filters applied to inertial platform repositioning." LAAS-CNRS, Toulouse, Research Report no. 92207, STCAN/DIGILOG-LAAS/CNRS Convention STCAN no. A.91.77.013, (94p.) September
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When analyzing an inverse problem, obtaining a maximum likelihood model is usually not sufficient, as normally information on the resolution power of the data is desired. In the general case many parameters are modeled, and an inspection of the
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are often used instead of random sampling from a space as they ensure even coverage and normally have a faster order of convergence than Monte Carlo simulations using random or pseudorandom sequences. Methods based on their use are called
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simulations and averaging the simulationsâ results. It has no restrictions on the probability distribution of the inputs to the simulations, requiring only that the inputs are randomly generated and are independent of each other and that
2914:. It has been applied with quasi-one-dimensional models to solve particle dynamics problems by efficiently exploring large configuration space. Reference is a comprehensive review of many issues related to simulation and optimization.
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or follow another desired distribution when a large enough number of elements of the sequence are considered is one of the simplest and most common ones. Weak correlations between successive samples are also often desirable/necessary.
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P. Del Moral, G. Rigal, and G. Salut. "Estimation and nonlinear optimal control: Particle resolution in filtering and estimation: Theoretical results". Convention DRET no. 89.34.553.00.470.75.01, Research report no.3 (123p.), October
4534:
P. Del Moral, G. Rigal, and G. Salut. "Estimation and nonlinear optimal control: Particle resolution in filtering and estimation: Experimental results". Convention DRET no. 89.34.553.00.470.75.01, Research report no.2 (54p.), January
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Monte Carlo method: Pouring out a box of coins on a table, and then computing the ratio of coins that land heads versus tails is a Monte Carlo method of determining the behavior of repeated coin tosses, but it is not a
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P. Del Moral, G. Rigal, and G. Salut. "Estimation and nonlinear optimal control: An unified framework for particle solutions". LAAS-CNRS, Toulouse, Research Report no. 91137, DRET-DIGILOG- LAAS/CNRS contract, April
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to Jack H. Hetherington in 1984. In molecular chemistry, the use of genetic heuristic-like particle methodologies (a.k.a. pruning and enrichment strategies) can be traced back to 1955 with the seminal work of
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P. Del Moral, J.-Ch. Noyer, G. Rigal, and G. Salut. "Particle filters in radar signal processing: detection, estimation and air targets recognition". LAAS-CNRS, Toulouse, Research report no. 92495, December
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failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically.
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Carmona, René; Del Moral, Pierre; Hu, Peng; Oudjane, Nadia (2012). "An
Introduction to Particle Methods with Financial Applications". In Carmona, René A.; Moral, Pierre Del; Hu, Peng; et al. (eds.).
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The net effect, over the course of many simulated games, is that the value of a node representing a move will go up or down, hopefully corresponding to whether or not that node represents a good move.
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Shojaeefard, M.H.; Khalkhali, A.; Yarmohammadisatri, Sadegh (2017). "An efficient sensitivity analysis method for modified geometry of
Macpherson suspension based on Pearson Correlation Coefficient".
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were two of the major organizations responsible for funding and disseminating information on Monte Carlo methods during this time, and they began to find a wide application in many different fields.
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In an effort to assess the impact of random number quality on Monte Carlo simulation outcomes, astrophysical researchers tested cryptographically secure pseudorandom numbers generated via Intel's
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The best-known importance sampling method, the Metropolis algorithm, can be generalized, and this gives a method that allows analysis of (possibly highly nonlinear) inverse problems with complex
1736:. No statistically significant difference was found between models generated with typical pseudorandom number generators and RDRAND for trials consisting of the generation of 10 random numbers.
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of pseudo-random uniform variables from the interval at one time, or once at many different times, and assigning values less than or equal to 0.50 as heads and greater than 0.50 as tails, is a
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1488:-type Monte Carlo methods for estimating particle transmission energies. Mean-field genetic type Monte Carlo methodologies are also used as heuristic natural search algorithms (a.k.a.
85:
Monte Carlo methods have been recognized as one of the most important and influential ideas of the 20th century, and they have enabled many scientific and technological breakthroughs.
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Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N.; Teller, Augusta H.; Teller, Edward (June 1, 1953). "Equation of State Calculations by Fast Computing Machines".
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required for further postwar development of nuclear weapons, including the design of the H-bomb, though severely limited by the computational tools at the time. Von Neumann,
2861:. These sequences "fill" the area better and sample the most important points more frequently, so quasi-Monte Carlo methods can often converge on the integral more quickly.
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Monte Carlo methods are also efficient in solving coupled integral differential equations of radiation fields and energy transport, and thus these methods have been used in
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A Monte Carlo approach was used for evaluating the potential value of a proposed program to help female petitioners in Wisconsin be successful in their applications for
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Int Panis, L.; De Nocker, L.; De Vlieger, I.; Torfs, R. (2001). "Trends and uncertainty in air pollution impacts and external costs of Belgian passenger car traffic".
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shows that the Monte Carlo analysis has a narrower range than the "what if" analysis. This is because the "what if" analysis gives equal weight to all scenarios (see
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Monte Carlo methods. "Indeed, the same computer code can be viewed simultaneously as a 'natural simulation' or as a solution of the equations by natural sampling."
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The standards for Monte Carlo experiments in statistics were set by Sawilowsky. In applied statistics, Monte Carlo methods may be used for at least four purposes:
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The approximation is generally poor if only a few points are randomly placed in the whole square. On average, the approximation improves as more points are placed.
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Chen, Shang-Ying; Hsu, Kuo-Chin; Fan, Chia-Ming (March 15, 2021). "Improvement of generalized finite difference method for stochastic subsurface flow modeling".
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Cunha Jr, A.; Nasser, R.; Sampaio, R.; Lopes, H.; Breitman, K. (2014). "Uncertainty quantification through the Monte Carlo method in a cloud computing setting".
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can be conducted (for instance: breaking bonds, introducing impurities at specific sites, changing the local/global structure, or introducing external fields).
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Bartels, Christian; Karplus, Martin (December 31, 1997). "Probability Distributions for Complex Systems: Adaptive Umbrella Sampling of the Potential Energy".
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Atanassova, E.; Gurov, T.; Karaivanova, A.; Ivanovska, S.; Durchova, M.; Dimitrov, D. (2016). "On the parallelization approaches for Intel MIC architecture".
2902:. The problem is to minimize (or maximize) functions of some vector that often has many dimensions. Many problems can be phrased in this way: for example, a
705:; Driels and Shin observe that âeven for sample sizes an order of magnitude lower than the number required, the calculation of that number is quite stable."
2792:, it can be estimated by randomly selecting points in 100-dimensional space, and taking some kind of average of the function values at these points. By the
5913:"Increasing Access to Restraining Orders for Low Income Victims of Domestic Violence: A Cost-Benefit Analysis of the Proposed Domestic Abuse Grant Program"
7000:
Int Panis, L.; Rabl, A.; De Nocker, L.; Torfs, R. (2002). Sturm, P. (ed.). "Diesel or Petrol ? An environmental comparison hampered by uncertainty".
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on Markov interpretations of a class of nonlinear parabolic partial differential equations arising in fluid mechanics. An earlier pioneering article by
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densities of interest may be impractical, or even useless. But it is possible to pseudorandomly generate a large collection of models according to the
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problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes:
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characterized by many unknown parameters, many of which are difficult to obtain experimentally. Monte Carlo simulation methods do not always require
2434:
To provide efficient random estimates of the Hessian matrix of the negative log-likelihood function that may be averaged to form an estimate of the
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Caffarel, Michel; Ceperley, David; Kalos, Malvin (1993). "Comment on FeynmanâKac Path-Integral Calculation of the Ground-State Energies of Atoms".
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Baeurle, Stephan A. (2009). "Multiscale modeling of polymer materials using field-theoretic methodologies: A survey about recent developments".
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Hill, Stacy D.; Spall, James C. (2019). "Stationarity and Convergence of the Metropolis-Hastings Algorithm: Insights into Theoretical Aspects".
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We know the expected value exists. The dice throws are randomly distributed and independent of each other. So simple Monte Carlo is applicable:
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GrĂŒne-Yanoff, T., & Weirich, P. (2010). The philosophy and epistemology of simulation: A review, Simulation & Gaming, 41(1), pp. 20-50
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Das, Sonjoy; Spall, James C.; Ghanem, Roger (2010). "Efficient Monte Carlo computation of Fisher information matrix using prior information".
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and many random simulations are used to estimate the long-term potential of each move. A black box simulator represents the opponent's moves.
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be the estimated variance, sometimes called the âsampleâ variance; it is the variance of the results obtained from a relatively small number
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Wei, J.; Kruis, F.E. (2013). "A GPU-based parallelized Monte-Carlo method for particle coagulation using an acceptanceârejection strategy".
2634:. It was proposed to help women succeed in their petitions by providing them with greater advocacy thereby potentially reducing the risk of
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interest and exchange rates, as well as the effect of distinct risk events like the cancellation of a contract or the change of a tax law.
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Monte Carlo methods provide a way out of this exponential increase in computation time. As long as the function in question is reasonably
1761:), while the Monte Carlo method hardly samples in the very low probability regions. The samples in such regions are called "rare events".
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detection (POD), which together will equal an overall probability of success (POS). Ultimately this serves as a practical application of
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Suppose we want to know how many times we should expect to throw three eight-sided dice for the total of the dice throws to be at least
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Milik, M.; Skolnick, J. (January 1993). "Insertion of peptide chains into lipid membranes: an off-lattice Monte Carlo dynamics model".
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Hill, R.; Healy, B.; Holloway, L.; Kuncic, Z.; Thwaites, D.; Baldock, C. (March 2014). "Advances in kilovoltage x-ray beam dosimetry".
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What this means depends on the application, but typically they should pass a series of statistical tests. Testing that the numbers are
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The theory of more sophisticated mean-field type particle Monte Carlo methods had certainly started by the mid-1960s, with the work of
350:. That is, in the limit, the samples being generated by the MCMC method will be samples from the desired (target) distribution. By the
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C. Forastero and L. Zamora and D. Guirado and A. Lallena (2010). "A Monte Carlo tool to simulate breast cancer screening programmes".
5485:
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Liu, Jun S.; Liang, Faming; Wong, Wing Hung (March 1, 2000). "The Multiple-Try Method and Local Optimization in Metropolis Sampling".
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In general, the Monte Carlo methods are used in mathematics to solve various problems by generating suitable random numbers (see also
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for sampling and computing the posterior distribution of a signal process given some noisy and partial observations using interacting
1492:) in evolutionary computing. The origins of these mean-field computational techniques can be traced to 1950 and 1954 with the work of
5950:"Perbandingan Penerbitan dan Harga Buku Mengikut Genre di Malaysia dan Jepun Menggunakan Data Akses Terbuka dan Simulasi Monte Carlo"
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Golden, Leslie M. (1979). "The Effect of Surface Roughness on the Transmission of Microwave Radiation Through a Planetary Surface".
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algorithms are used to transform uniformly distributed pseudo-random numbers into numbers that are distributed according to a given
8766:
5852:"A Monte Carlo simulation approach for estimating the health and economic impact of interventions provided at a student-run clinic"
2773:. Second, the boundary of a multidimensional region may be very complicated, so it may not be feasible to reduce the problem to an
2342:, or for studying biological systems such as genomes, proteins, or membranes. The systems can be studied in the coarse-grained or
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program could be seen as trying to find the set of, say, 10 moves that produces the best evaluation function at the end. In the
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Gordon, N.J.; Salmond, D.J.; Smith, A.F.M. (April 1993). "Novel approach to nonlinear/non-Gaussian Bayesian state estimation".
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Crisan, Dan; Gaines, Jessica; Lyons, Terry (1998). "Convergence of a branching particle method to the solution of the Zakai".
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3998:"Branching and interacting particle systems approximations of FeynmanâKac formulae with applications to non-linear filtering"
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frameworks depending on the desired accuracy. Computer simulations allow monitoring of the local environment of a particular
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evolution and microwave radiation transmission through a rough planetary surface. Monte Carlo methods are also used in the
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is more recent. It was in 1993, that Gordon et al., published in their seminal work the first application of a Monte Carlo
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invented the modern version of the Markov Chain Monte Carlo method while he was working on nuclear weapons projects at the
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Del Moral, Pierre; Guionnet, Alice (1999). "On the stability of Measure Valued Processes with Applications to filtering".
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Popular exposition of the Monte Carlo Method was conducted by McCracken. The method's general philosophy was discussed by
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234:, which are far quicker to use than the tables of random numbers that had been previously used for statistical sampling.
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Elishakoff, I., (2003) Notes on Philosophy of the Monte Carlo Method, International Applied Mechanics, 39(7), pp.753-762
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Lin, Y.; Wang, F.; Liu, B. (2018). "Random number generators for large-scale parallel Monte Carlo simulations on FPGA".
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2181:. The need arises from the interactive, co-linear and non-linear behavior of typical process simulations. For example,
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MEZEI, M (December 31, 1986). "Adaptive umbrella sampling: Self-consistent determination of the non-Boltzmann bias".
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Chaslot, Guillaume M. J. -B; Winands, Mark H. M.; Van Den Herik, H. Jaap (2008). "Parallel Monte-Carlo Tree Search".
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convergenceâi.e., quadrupling the number of sampled points halves the error, regardless of the number of dimensions.
1953:
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Möller, W.; Eckstein, W. (March 1, 1984). "Tridyn â A TRIM simulation code including dynamic composition changes".
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twiceâor more frequentlyâfor the efficiency of not having to track which permutations have already been selected).
2409:, infinite sample size and infinitesimally small treatment effect), real data often do not have such distributions.
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the (pseudo-random) number generator has certain characteristics (e.g. a long "period" before the sequence repeats)
1389:
first experimented with the Monte Carlo method while studying neutron diffusion, but he did not publish this work.
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Kroese, D. P.; Brereton, T.; Taimre, T.; Botev, Z. I. (2014). "Why the Monte Carlo method is so important today".
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Monte Carlo methods are also a compromise between approximate randomization and permutation tests. An approximate
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exists), but does not have a formula available to compute it. The simple Monte Carlo method gives an estimate for
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In principle, Monte Carlo methods can be used to solve any problem having a probabilistic interpretation. By the
6930:"Monte Carlo Simulations of Proteins in Cages: Influence of Confinement on the Stability of Intermediate States"
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An alternate formula can be used in the special case where all simulation results are bounded above and below.
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7180:. Neural Information Processing Systems 2010. Neural Information Processing Systems Foundation. Archived from
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Benov, Dobriyan M. (2016). "The Manhattan Project, the first electronic computer and the Monte Carlo method".
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and power properties of statistics can be calculated for data drawn from classical theoretical distributions (
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4078:"Particle approximations of Lyapunov exponents connected to Schrödinger operators and FeynmanâKac semigroups"
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Spall, James C. (2005). "Monte Carlo Computation of the Fisher Information Matrix in Nonstandard Settings".
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Hastings, W. K. (April 1, 1970). "Monte Carlo sampling methods using Markov chains and their applications".
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Uses of Monte Carlo methods require large amounts of random numbers, and their use benefitted greatly from
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sequences, making it easy to test and re-run simulations. The only quality usually necessary to make good
1413:
Being secret, the work of von Neumann and Ulam required a code name. A colleague of von Neumann and Ulam,
712:
in one pass while minimizing the possibility that accumulated numerical error produces erroneous results:
9647:
9608:
9440:
9241:
9165:
8466:
8220:
7889:
7353:
5162:
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms
4577:"Measure Valued Processes and Interacting Particle Systems. Application to Non Linear Filtering Problems"
3045:
3005:
2298:
379:
1429:
where Ulam's uncle would borrow money from relatives to gamble. Monte Carlo methods were central to the
1013:
simulations can be run âfrom scratch,â or, since k simulations have already been done, one can just run
9325:
9297:
9292:
9040:
8799:
8705:
8685:
8593:
8304:
8122:
7605:
7477:
7014:
5319:
3400:
3020:
3010:
2918:
2907:
2899:
2573:
in order to provide the swiftest and most expedient method of rescue, saving both lives and resources.
2219:
2126:
1848:
1481:
1378:
185:
The ratio of the inside-count and the total-sample-count is an estimate of the ratio of the two areas,
5310:
4371:
Kitagawa, G. (1996). "Monte carlo filter and smoother for non-Gaussian nonlinear state space models".
2910:
the goal is to minimize distance traveled. There are also applications to engineering design, such as
9057:
8825:
8546:
8471:
8400:
8329:
8249:
8237:
8107:
8095:
8088:
7796:
7517:
2877:
2278:, Monte Carlo simulation is used to compute system-level response given the component-level response.
1903:
1713:
367:
281:
182:
Count the number of points inside the quadrant, i.e. having a distance from the origin of less than 1
5802:
5549:
4734:
2684:: a human can be declared unintelligent if their writing cannot be told apart from a generated one.
1526:
path integrals. The origins of Quantum Monte Carlo methods are often attributed to Enrico Fermi and
9540:
9307:
9170:
8855:
8820:
8784:
8569:
8011:
7920:
7879:
7791:
7482:
7321:
6327:
5583:
5426:
4593:
3872:
3075:
2935:
2865:
2858:
2854:
2693:
2570:
2249:
2114:
1883:
1749:
1718:
1707:
1385:
can be estimated by dropping needles on a floor made of parallel equidistant strips. In the 1930s,
1350:
nature of the algorithm allows this large cost to be reduced (perhaps to a feasible level) through
339:
335:
259:
105:
6587:
4587:(2) (Publications du Laboratoire de Statistique et ProbabilitĂ©s, 96-15 (1996) ed.): 438â495.
2650:
Monte Carlo approach had also been used to simulate the number of book publications based on book
9449:
9062:
9002:
8939:
8577:
8561:
8299:
8161:
8151:
8001:
7915:
7046:
6266:
Markov Chain Monte Carlo Simulations and Their Statistical Analysis (With Web-Based Fortran Code)
4780:"On the stability of interacting processes with applications to filtering and genetic algorithms"
4576:
2893:
2770:
2705:
2464:
2458:
2421:
2275:
1943:
1898:
1853:
1816:
1806:
1754:
1594:
1555:
1347:
1118:< 100 be the desired confidence level, expressed as a percentage. Let every simulation result
285:
112:
55:
6909:
5796:. Springer Proceedings in Mathematics. Vol. 12. Springer Berlin Heidelberg. pp. 3â49.
2614:
at a business unit or corporate level, or other financial valuations. They can be used to model
9487:
9417:
9210:
9147:
8902:
8789:
7786:
7683:
7590:
7469:
7368:
7086:
6322:
5919:
5797:
5739:"Search Modeling and Optimization in USCG's Search and Rescue Optimal Planning System (SAROPS)"
5679:
5544:
5421:
4588:
3793:
McKean, Henry P. (1967). "Propagation of chaos for a class of non-linear parabolic equations".
2898:
Another powerful and very popular application for random numbers in numerical simulation is in
2598:
2354:
is happening for instance. In cases where it is not feasible to conduct a physical experiment,
2090:
1641:
411:
315:
and schedule overruns are routinely better than human intuition or alternative "soft" methods.
6747:; Rosenbluth, Arianna W.; Rosenbluth, Marshall N.; Teller, Augusta H.; Teller, Edward (1953).
2864:
Another class of methods for sampling points in a volume is to simulate random walks over it (
2137:
is usually based on a Monte Carlo approach to select the next colliding atom. In experimental
272:, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see
9512:
9454:
9397:
9223:
9116:
9025:
8751:
8635:
8494:
8486:
8376:
8368:
8183:
8079:
8057:
8016:
7981:
7948:
7894:
7869:
7824:
7763:
7723:
7525:
7348:
7181:
2793:
2761:
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2252:
can determine the position of a robot. It is often applied to stochastic filters such as the
2082:
1893:
1788:
1585:
1536:
1515:
1505:
366:
whose transition probabilities depend on the distributions of the current random states (see
265:
In physics-related problems, Monte Carlo methods are useful for simulating systems with many
255:
28:
20:
6575:
3159:
2532:
computations that produce photo-realistic images of virtual 3D models, with applications in
2467:
that is useful for searching for the best move in a game. Possible moves are organized in a
2385:
To compare competing statistics for small samples under realistic data conditions. Although
2373:, making it one of the most physically accurate 3D graphics rendering methods in existence.
9435:
9010:
8959:
8935:
8897:
8815:
8794:
8746:
8625:
8603:
8572:
8481:
8358:
8309:
8227:
8200:
8156:
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7874:
7650:
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7248:
7176:. In Lafferty, J.; Williams, C. K. I.; Shawe-Taylor, J.; Zemel, R. S.; Culotta, A. (eds.).
7009:
Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (1996) .
6941:
6893:
6760:
6657:
6610:
6583:
6472:
6425:
6013:
5911:
Elwart, Liz; Emerson, Nina; Enders, Christina; Fumia, Dani; Murphy, Kevin (December 2006).
5865:
5642:
5276:
5239:
5169:
5107:
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3924:
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3649:
3606:
3561:
3245:
3186:
2948:
2676:
2478:
Starting at root node of the tree, select optimal child nodes until a leaf node is reached.
2431:. This sample then approximates and summarizes all the essential features of the posterior.
2420:(which are often impossible to compute) while being more accurate than critical values for
2215:
2170:
2154:
2019:
1888:
1497:
319:
273:
66:
6066:
Del Moral, Pierre; Doucet, Arnaud; Jasra, Ajay (2006). "Sequential Monte Carlo samplers".
3520:"Determining the number of Iterations for Monte Carlo Simulations of Weapon Effectiveness"
2781:
is by no means unusual, since in many physical problems, a "dimension" is equivalent to a
2101:
forms as well as in modeling radiation transport for radiation dosimetry calculations. In
134:
8:
9582:
9507:
9430:
9111:
8875:
8868:
8830:
8738:
8718:
8690:
8423:
8289:
8284:
8274:
8266:
8084:
8045:
7935:
7925:
7834:
7613:
7569:
7487:
7412:
7314:
7202:
Monte Carlo Methods in Global Illumination - Photo-realistic Rendering with Randomization
6796:
6744:
6725:
6576:
6319:
Papers from the international symposium on Symbolic and algebraic computation - ISSAC '92
6181:
4425:
3035:
2839:
2834:
2681:
2529:
2398:
2245:
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2118:
2102:
2034:
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1532:
1527:
1511:
1462:
1434:
1414:
1371:
304:
33:
6945:
6897:
6764:
6494:
An Introduction to Computer Simulation Methods, Part 2, Applications to Physical Systems
6476:
6429:
6415:
6017:
5869:
5646:
5280:
5243:
5173:
5111:
5060:
5007:
4934:
4866:
4795:
4470:
4296:
4225:
4179:
4129:
3829:
3688:
3653:
3610:
3565:
3249:
3190:
2714:
Monte-Carlo integration works by comparing random points with the value of the function.
9596:
9407:
9261:
9157:
9106:
8982:
8879:
8863:
8840:
8617:
8351:
8334:
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8205:
8100:
8062:
8033:
7993:
7953:
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7502:
7497:
7109:
6962:
6929:
6865:
6820:
6784:
6694:
6449:
6350:
6305:
6252:
6223:
6193:
6185:
6148:
McCracken, D. D., (1955) The Monte Carlo Method, Scientific American, 192(5), pp. 90-97
6112:
Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control
6093:
6075:
5972:
5888:
5851:
5439:
5292:
5131:
5080:
5024:
4991:
4948:
4920:
4878:
4715:
4674:
4633:
4482:
4388:
4353:
4310:
4212:
Hetherington, Jack H. (1984). "Observations on the statistical iteration of matrices".
3775:
3622:
3596:
3470:
3452:
3374:
3312:
3269:
3218:
3140:
3030:
2996:
2615:
2443:
2435:
2428:
2370:
2355:
2286:
2268:
2212:
2189:, Monte Carlo methods are applied to analyze correlated and uncorrelated variations in
2110:
2086:
1981:
1774:
1551:
1458:
1422:
1351:
269:
266:
70:
6675:
MacGillivray, H. T.; Dodd, R. J. (1982). "Monte-Carlo simulations of galaxy systems".
6437:
5119:
5068:
5015:
4803:
4779:
4061:
4044:
3848:
3813:
9591:
9502:
9472:
9464:
9284:
9275:
9200:
9131:
8987:
8972:
8947:
8835:
8776:
8642:
8630:
8256:
8173:
8117:
8040:
7884:
7806:
7585:
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7252:
7229:
7205:
7126:
7071:
7052:
7018:
6967:
6857:
6828:
6776:
6711:
6698:
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6591:
6556:
6535:
6497:
6484:
6441:
6402:
6367:
6340:
6291:
6269:
6256:
6089:
6025:
5976:
5893:
5815:
5658:
5562:
5323:
5296:
5181:
5123:
5098:
Rogers, D.W.O. (2006). "Fifty years of Monte Carlo simulations for medical physics".
5072:
5029:
4952:
4882:
4719:
4678:
4345:
4191:
4141:
4015:
3970:
3853:
3466:
3420:
3316:
3304:
3261:
3210:
3202:
2990:
2939:
2774:
2769:
points are needed for 100 dimensionsâfar too many to be computed. This is called the
2565:
2503:
2417:
2351:
2323:
2302:
2282:
2142:
2122:
2024:
1999:
1971:
1658:
1598:
1547:
1485:
375:
355:
6729:
6453:
6382:
6354:
6227:
6097:
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5135:
5084:
4637:
4486:
4357:
4314:
3779:
3626:
3474:
3378:
3273:
3144:
1769:
Monte Carlo methods are especially useful for simulating phenomena with significant
1661:, unpredictability is vital). Many of the most useful techniques use deterministic,
74:
9527:
9482:
9246:
9233:
9126:
9101:
9035:
8967:
8845:
8453:
8346:
8279:
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7829:
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7507:
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6215:
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6048:
6021:
5964:
5883:
5873:
5850:
Arenas, Daniel J.; Lett, Lanair A.; Klusaritz, Heather; Teitelman, Anne M. (2017).
5807:
5650:
5554:
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5284:
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5019:
5011:
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4337:
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4089:
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3300:
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3253:
3222:
3194:
3132:
2639:
2186:
2138:
2134:
2009:
1976:
1858:
1729:
1687:
the (pseudo-random) number generator produces values that pass tests for randomness
1466:
1406:
1346:
sample is high. Although this is a severe limitation in very complex problems, the
668:
170:
5949:
4874:
4006:. Lecture Notes in Mathematics. Vol. 1729. Berlin: Springer. pp. 1â145.
9444:
9188:
9050:
8977:
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8499:
8476:
8445:
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8067:
8021:
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7402:
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5654:
4025:
2931:
2881:
2847:
2290:
2257:
1863:
1519:
371:
351:
308:
223:
If the points are not uniformly distributed, then the approximation will be poor.
58:
8934:
7160:
6953:
5811:
5558:
4694:"A particle approximation of the solution of the KushnerâStratonovitch equation"
4450:
Carvalho, Himilcon; Del Moral, Pierre; Monin, André; Salut, Gérard (July 1997).
4187:
4001:
3519:
3443:
Del Moral, P.; Doucet, A.; Jasra, A. (2006). "Sequential Monte Carlo samplers".
1669:
is for the pseudo-random sequence to appear "random enough" in a certain sense.
9393:
9388:
7851:
7781:
7427:
6800:
5470:
4943:
4908:
3910:
3755:
3080:
3025:
2903:
2873:
2651:
2557:
2234:
2226:
2014:
2004:
1948:
1908:
1680:
Sawilowsky lists the characteristics of a high-quality Monte Carlo simulation:
1470:
1393:
1021:
more simulations and add their results into those from the sample simulations:
404:
363:
323:
6248:
5387:
5288:
4629:
4602:
3696:
3661:
3618:
2718:
1796:
1739:
1583:
should be defined. For example, Ripley defines most probabilistic modeling as
1518:
can also be interpreted as a mean-field particle Monte Carlo approximation of
9636:
9550:
9517:
9380:
9341:
9152:
9121:
8585:
8539:
8144:
7846:
7673:
7437:
7432:
6992:
5637:
Lorentz, Richard J. (2011). "Improving MonteâCarlo Tree Search in Havannah".
5374:
Cassey; Smith (2014). "Simulating confidence for the Ellison-Glaeser Index".
4349:
4341:
4233:
4137:
3496:
3370:
3343:
3308:
3265:
3257:
3206:
3065:
2253:
2208:
2204:
2190:
2174:
2145:, understanding their behavior and comparing experimental data to theory. In
2089:, and related applied fields, and have diverse applications from complicated
1489:
1450:
1441:
computer to perform the first fully automated Monte Carlo calculations, of a
1367:
5435:
4281:"Monte-Carlo calculations of the average extension of macromolecular chains"
3945:(1957). "Symbiogenetic evolution processes realized by artificial methods".
2487:
Use the results of that simulated game to update the node and its ancestors.
9492:
9425:
9402:
9317:
8647:
7943:
7841:
7776:
7718:
7703:
7640:
7595:
6971:
6853:
6832:
6445:
6219:
5968:
5897:
5252:
5227:
5127:
5076:
5033:
4195:
4145:
3857:
3838:
3814:"A class of Markov processes associated with nonlinear parabolic equations"
2789:
2537:
2394:
2386:
2366:
2230:
2194:
2146:
2098:
1733:
1477:
1445:
core, in the spring of 1948. In the 1950s Monte Carlo methods were used at
1386:
1354:
strategies in local processors, clusters, cloud computing, GPU, FPGA, etc.
343:
312:
251:
6861:
6512:
6336:
4710:
4693:
4669:
4652:
3966:
FeynmanâKac formulae. Genealogical and interacting particle approximations
9535:
9497:
9180:
9081:
8943:
8756:
8723:
8215:
8132:
8127:
7771:
7728:
7708:
7688:
7678:
7447:
6283:
6080:
4094:
3771:
3737:
3735:
3457:
2518:
2494:
Monte Carlo Tree Search has been used successfully to play games such as
2468:
2347:
2094:
2029:
1770:
1496:
on genetic type mutation-selection learning machines and the articles by
1493:
1364:
378:. In contrast with traditional Monte Carlo and MCMC methodologies, these
292:
247:
138:
48:
7105:
6312:. Acta Numerica. Vol. 7. Cambridge University Press. pp. 1â49.
1728:
instruction set, as compared to those derived from algorithms, like the
8381:
7861:
7561:
7492:
7442:
7417:
7337:
6824:
6690:
5680:"Arimaa challenge â comparison study of MCTS versus alpha-beta methods"
5641:. Lecture Notes in Computer Science. Vol. 6515. pp. 105â115.
4392:
4011:
2976:
2533:
2402:
1666:
1602:
1430:
62:
7002:
Mitteilungen Institut fĂŒr Verbrennungskraftmaschinen und Thermodynamik
6905:
6780:
6772:
6052:
4305:
4280:
3756:"Los Alamos Bets on ENIAC: Nuclear Monte Carlo Simulations, 1947-1948"
3732:
3573:
3214:
3198:
3136:
1296:{\displaystyle n\geq 2(b-a)^{2}\ln(2/(1-(\delta /100)))/\epsilon ^{2}}
8534:
8386:
8006:
7801:
7713:
7698:
7693:
7658:
6632:
6578:
How to Measure Anything: Finding the Value of Intangibles in Business
5543:. Lecture Notes in Computer Science. Vol. 5131. pp. 60â71.
4852:
4735:"Discrete filtering using branching and interacting particle systems"
4478:
3426:
2778:
2495:
2241:
method in combination with highly efficient computational algorithms.
671:â the percent chance that, when the Monte Carlo algorithm completes,
122:
51:
6743:
6651:
5720:"How the Coast Guard Uses Analytics to Search for Those Lost at Sea"
5584:
Monte-Carlo Tree Search in the game of Tantrix: Cosc490 Final Report
5484:
Chaslot, Guillaume; Bakkes, Sander; Szita, Istvan; Spronck, Pieter.
4384:
3176:
1377:
An early variant of the Monte Carlo method was devised to solve the
334:
the 'sample mean') of independent samples of the variable. When the
311:, aircraft design, etc.), Monte Carloâbased predictions of failure,
73:
in Monaco, where the primary developer of the method, mathematician
8050:
7668:
7545:
7540:
7535:
5856:
4925:
3601:
3551:
2656:
2560:
utilizes Monte Carlo methods within its computer modeling software
1523:
382:
techniques rely on sequential interacting samples. The terminology
300:
97:
Monte Carlo methods vary, but tend to follow a particular pattern:
5517:
5343:
5228:"A Scalar optimized parallel implementation of the DSMC technique"
1640:
Convergence of the Monte Carlo simulation can be checked with the
1094:
9555:
9256:
6978:
6607:
The Failure of Risk Management: Why It's Broken and How to Fix It
2499:
1454:
684:
243:
7228:. Philadelphia: Society for Industrial and Applied Mathematics.
7011:
Numerical Recipes in Fortran 77: The Art of Scientific Computing
7008:
6928:
Ojeda, P.; Garcia, M.; Londono, A.; Chen, N.Y. (February 2009).
5992:
3897:
Turing, Alan M. (1950). "Computing machinery and intelligence".
3330:
Spall, J. C. (2003). "Estimation via Markov Chain Monte Carlo".
2463:
Monte Carlo methods have been developed into a technique called
1560:
299:
in business and, in mathematics, evaluation of multidimensional
9477:
8458:
8432:
8412:
7663:
7454:
7295:
7266:
Mazhdrakov, Metodi; Benov, Dobriyan; Valkanov, Nikolai (2018).
4045:"A Moran particle system approximation of FeynmanâKac formulae"
2766:
2710:
2564:
in order to calculate the probable locations of vessels during
2561:
2541:
2511:
2150:
1725:
1426:
4111:"Diffusion Monte Carlo Methods with a fixed number of walkers"
2427:
To provide a random sample from the posterior distribution in
722:= 0; run the simulation for the first time, producing result
61:
to obtain numerical results. The underlying concept is to use
7306:
6115:
2660:
1438:
395:
that the statistical interaction between particles vanishes.
338:
of the variable is parameterized, mathematicians often use a
7004:. Heft 81 Vol 1. Technische UniversitĂ€t Graz Austria: 48â54.
5849:
5216:
G. A. Bird, Molecular Gas Dynamics, Clarendon, Oxford (1976)
4992:"GPU-based high-performance computing for radiation therapy"
7397:
6999:
6749:"Equation of State Calculations by Fast Computing Machines"
5538:
4449:
4109:
Assaraf, Roland; Caffarel, Michel; Khelif, Anatole (2000).
3969:. Probability and Its Applications. Springer. p. 575.
2967:
information and data with an arbitrary noise distribution.
2938:
in the model space. This probability distribution combines
2635:
2545:
2315:
296:
291:
Other examples include modeling phenomena with significant
6739:(1987 Special Issue dedicated to Stanislaw Ulam): 125â130.
5766:
3586:
2474:
The Monte Carlo tree search (MCTS) method has four steps:
342:(MCMC) sampler. The central idea is to design a judicious
326:
of some random variable can be approximated by taking the
7013:. Fortran Numerical Recipes. Vol. 1 (2nd ed.).
6383:"Stan Ulam, John von Neumann, and the Monte Carlo method"
5790:
5700:
5355:
3710:
3708:
3706:
3122:
2149:, they are used in such diverse manners as to model both
307:. In application to systems engineering problems (space,
126:
Monte Carlo method applied to approximating the value of
6362:
Doucet, Arnaud; Freitas, Nando de; Gordon, Neil (2001).
6317:
Davenport, J. H. (1992). "Primality testing revisited".
5910:
4279:
Rosenbluth, Marshall N.; Rosenbluth, Arianna W. (1955).
3873:"Estimation of particle transmission by random sampling"
3158:
Hubbard, Douglas; Samuelson, Douglas A. (October 2009).
3104:
7265:
6879:"Monte Carlo sampling of solutions to inverse problems"
5737:
Stone, Lawrence D.; Kratzke, Thomas M.; Frost, John R.
5046:
3795:
Lecture Series in Differential Equations, Catholic Univ
3741:
2309:
2169:
Monte Carlo methods are widely used in engineering for
986:
sufficient sample simulations were done to ensure that
160:
6927:
5486:"Monte-Carlo Tree Search: A New Framework for Game AI"
5349:
3754:
Haigh, Thomas; Priestley, Mark; Rope, Crispin (2014).
3703:
2880:, and interacting type MCMC methodologies such as the
2803:
2729:
1657:
to be useful (although, for some applications such as
5483:
4733:
Crisan, Dan; Del Moral, Pierre; Lyons, Terry (1999).
4459:
IEEE Transactions on Aerospace and Electronic Systems
4452:"Optimal Non-linear Filtering in GPS/INS Integration"
4411:"Non Linear Filtering: Interacting Particle Solution"
4165:
4108:
3927:(1954). "Esempi numerici di processi di evoluzione".
2802:
2728:
2674:
writes about Monte Carlo generators in his 2001 book
1696:
the algorithm used is valid for what is being modeled
1197:
1106:
that is twice the maximum allowed difference between
914:
642:
354:, the stationary distribution is approximated by the
9219:
Autoregressive conditional heteroskedasticity (ARCH)
7178:
Advances in Neural Information Processing Systems 23
6065:
4990:
Jia, Xun; Ziegenhein, Peter; Jiang, Steve B (2014).
4909:"Radio-flaring Ultracool Dwarf Population Synthesis"
4732:
4278:
3720:
3442:
2986:
2481:
Expand the leaf node and choose one of its children.
2452:
2233:, where the Boltzmann equation is solved for finite
1484:
and Herman Kahn, published in 1951, used mean-field
6529:
6399:
Monte Carlo: Concepts, Algorithms, and Applications
6361:
4249:"Note on census-taking in Monte Carlo calculations"
3041:
List of software for Monte Carlo molecular modeling
1748:By contrast, Monte Carlo simulations sample from a
1690:
there are enough samples to ensure accurate results
443:; more formally, it will be the case that, for any
8681:
7123:Statistics via Monte Carlo Simulation with Fortran
6876:
6620:Judgement under Uncertainty: Heuristics and Biases
6288:The Monte Carlo Method in Condensed Matter Physics
6126:
6068:Journal of the Royal Statistical Society, Series B
5904:
4989:
4971:
4959:
4653:"Nonlinear filtering and measure-valued processes"
4327:
3753:
3536:
3445:Journal of the Royal Statistical Society, Series B
3431:Monographs on Statistics & Applied Probability
2822:
2748:
2334:Monte Carlo methods are used in various fields of
2264:(simultaneous localization and mapping) algorithm.
1777:degrees of freedom. Areas of application include:
1732:, in Monte Carlo simulations of radio flares from
1295:
957:
7120:
7070:(2nd ed.). New York: John Wiley & Sons.
6649:
5834:
5414:Journal of Computational and Graphical Statistics
5400:
4777:
4758:
4615:
4373:Journal of Computational and Graphical Statistics
3422:Mean field simulation for Monte Carlo integration
2416:that are more efficient than exact tests such as
1740:Monte Carlo simulation versus "what if" scenarios
1647:
9634:
7269:The Monte Carlo Method. Engineering Applications
7121:Sawilowsky, Shlomo S.; Fahoome, Gail C. (2003).
7065:
6674:
5835:Kroese, D. P.; Taimre, T.; Botev, Z. I. (2011).
5194:
3518:Driels, Morris R.; Shin, Young S. (April 2004).
3157:
179:scatter a given number of points over the square
165:can be approximated using a Monte Carlo method:
8767:Multivariate adaptive regression splines (MARS)
6805:Journal of the American Statistical Association
6650:Kroese, D. P.; Taimre, T.; Botev, Z.I. (2011).
6617:
4330:IEE Proceedings F - Radar and Signal Processing
3289:Journal of the American Statistical Association
1095:A formula when simulations' results are bounded
77:, was inspired by his uncle's gambling habits.
6795:
6510:
6491:
6038:
5456:
5312:Climate Change 2013 The Physical Science Basis
5159:
4246:
4042:
3995:
3870:
2887:
2484:Play a simulated game starting with that node.
2113:, and Monte Carlo methods are used to compute
1745:variable are chosen and the results recorded.
7322:
7199:
7147:Journal of Modern Applied Statistical Methods
7044:
6839:
6627:Kalos, Malvin H.; Whitlock, Paula A. (2008).
6626:
6511:Grinstead, Charles; Snell, J. Laurie (1997).
5736:
5706:
5361:
4841:
4826:
4824:
4247:Fermi, Enrique; Richtmyer, Robert D. (1948).
3110:
2211:, Monte Carlo methods underpin the design of
2141:, Monte Carlo methods are used for designing
2056:
1632:of the behavior of repeatedly tossing a coin.
7168:
6877:Mosegaard, Klaus; Tarantola, Albert (1995).
6530:Hammersley, J. M.; Handscomb, D. C. (1975).
5459:Computational Statistics & Data Analysis
5225:
4211:
3286:
1759:quantifying uncertainty in corporate finance
958:{\displaystyle n\geq s^{2}/(z\epsilon )^{2}}
5373:
4778:Del Moral, Pierre; Guionnet, Alice (2001).
4691:
4650:
4049:Stochastic Processes and Their Applications
3394:
1409:, and we began to plan actual calculations.
7367:
7329:
7315:
7139:
6724:
6364:Sequential Monte Carlo methods in practice
5266:
4830:
4821:
4069:
4043:Del Moral, Pierre; Miclo, Laurent (2000).
3941:
3923:
3871:Herman, Kahn; Theodore, Harris E. (1951).
3714:
3674:
3524:Naval Postgraduate School Technical Report
3517:
3056:Monte Carlo methods for electron transport
2823:{\displaystyle \scriptstyle 1/{\sqrt {N}}}
2749:{\displaystyle \scriptstyle 1/{\sqrt {N}}}
2081:Monte Carlo methods are very important in
2063:
2049:
1795:
1453:, and became popularized in the fields of
358:of the random states of the MCMC sampler.
7980:
7218:
7159:
7066:Rubinstein, R. Y.; Kroese, D. P. (2007).
6961:
6730:"The beginning of the Monte Carlo method"
6326:
6316:
6310:Monte Carlo and quasi-Monte Carlo methods
6137:
6079:
5887:
5877:
5801:
5548:
5425:
5251:
5023:
4942:
4924:
4895:
4709:
4668:
4592:
4574:
4408:
4404:
4402:
4304:
4159:
4102:
4093:
4075:
4060:
3991:
3989:
3962:
3847:
3837:
3600:
3456:
3418:
3356:
2316:Intergovernmental Panel on Climate Change
2077:Monte Carlo method in statistical physics
889:Note that, when the algorithm completes,
141:. Given that the ratio of their areas is
7084:
6705:
6548:
6380:
6304:
6186:"Metropolis, Monte Carlo and the MANIAC"
6180:
5988:
5986:
5599:
4370:
3726:
3639:
3537:Shonkwiler, R. W.; Mendivil, F. (2009).
3498:Monte Carlo Theory, Methods and Examples
3235:
2717:
2709:
2329:
2117:of simple particle and polymer systems.
1699:it simulates the phenomenon in question.
690:corresponding to that confidence level.
219:There are two important considerations:
121:
27:
7087:"Risk Analysis in Investment Appraisal"
6981:International Journal of Vehicle Design
6604:
6573:
6552:Practical Guide to Computer Simulations
6396:
6234:
5948:Dahlan, Hadi Akbar (October 29, 2021).
5636:
5148:
3958:
3956:
3760:IEEE Annals of the History of Computing
3414:
3412:
3410:
3390:
3388:
3051:Monte Carlo method for photon transport
2576:
203:. Multiply the result by 4 to estimate
16:Probabilistic problem-solving algorithm
9635:
9293:KaplanâMeier estimator (product limit)
7171:"Monte-Carlo Planning in Large POMDPs"
7031:
6492:Gould, Harvey; Tobochnik, Jan (1988).
6460:
6282:
5947:
5602:"Monte-Carlo Planning in Large POMDPs"
5205:
5097:
4816:
4810:
4399:
4264:Declassified report Los Alamos Archive
4207:
4205:
4036:
3986:
3896:
3811:
3792:
2833:A refinement of this method, known as
2591:Monte Carlo methods for option pricing
1340:
242:Monte Carlo methods are often used in
69:in principle. The name comes from the
9366:
8933:
8680:
7979:
7749:
7366:
7310:
7068:Simulation and the Monte Carlo Method
6205:
6003:
5983:
5411:
4906:
4846:
4835:
4698:Probability Theory and Related Fields
4657:Probability Theory and Related Fields
4274:
4272:
3786:
3747:
3742:Mazhdrakov, Benov & Valkanov 2018
3513:
3511:
3490:
3488:
3486:
3484:
3329:
3061:Monte Carlo N-Particle Transport Code
2912:multidisciplinary design optimization
2687:
2523:
2376:
1693:the proper sampling technique is used
398:
391:
331:
295:in inputs such as the calculation of
9603:
9303:Accelerated failure time (AFT) model
7242:
7169:Silver, David; Veness, Joel (2010).
7051:(2nd ed.). New York: Springer.
6268:. Hackensack, NJ: World Scientific.
6263:
6208:Monte Carlo Methods and Applications
5828:
4977:
4965:
4784:Annales de l'Institut Henri Poincaré
4771:
4752:
3981:Series: Probability and Applications
3953:
3530:
3494:
3407:
3385:
2846:, adaptive umbrella sampling or the
2587:Quasi-Monte Carlo methods in finance
2551:
2361:
2310:Climate change and radiative forcing
1780:
1755:triangular probability distributions
9615:
8898:Analysis of variance (ANOVA, anova)
7750:
7245:Risk Analysis, A Quantitative Guide
6041:The Journal of Physical Chemistry B
4742:Markov Processes and Related Fields
4726:
4618:SIAM Journal on Applied Mathematics
4609:
4568:
4418:Markov Processes and Related Fields
4202:
3539:Explorations in Monte Carlo Methods
3504:. Work in progress. pp. 15â36.
2925:
2109:is an alternative to computational
1597:and Monte Carlo statistical tests.
462:Typically, the algorithm to obtain
386:reflects the fact that each of the
348:stationary probability distribution
13:
8993:CochranâMantelâHaenszel statistics
7619:Pearson product-moment correlation
6803:(1949). "The Monte Carlo Method".
6618:Kahneman, D.; Tversky, A. (1982).
4907:Route, Matthew (August 10, 2017).
4692:Crisan, Dan; Lyons, Terry (1999).
4651:Crisan, Dan; Lyons, Terry (1997).
4269:
4082:ESAIM Probability & Statistics
3508:
3481:
2953:posterior probability distribution
2645:
701:of âsampleâ simulations. Choose a
650:
101:Define a domain of possible inputs
14:
9694:
7288:
6237:Journal of Mathematical Chemistry
5581:
5514:"Monte Carlo Tree Search - About"
3996:Del Moral, P.; Miclo, L. (2000).
3880:Natl. Bur. Stand. Appl. Math. Ser
3526:(March 2003 - March 2004): 10â11.
2632:domestic abuse restraining orders
2548:, and cinematic special effects.
2453:Artificial intelligence for games
2318:relies on Monte Carlo methods in
2295:sequential Monte Carlo techniques
1169:. To have confidence of at least
708:The following algorithm computes
643:Determining a sufficiently large
9614:
9602:
9590:
9577:
9576:
9367:
7294:
7142:"You think you've got trivials?"
7045:Robert, C.; Casella, G. (2004).
6708:Stochastic Simulation in Physics
6160:
6151:
6142:
6131:
6120:
6104:
6090:10.1111/j.1467-9868.2006.00553.x
6006:Journal of Computational Physics
5767:"Project Risk Simulation (BETA)"
5677:
5269:Journal of Computational Physics
5232:Journal of Computational Physics
3677:Journal of Computational Physics
3467:10.1111/j.1467-9868.2006.00553.x
2989:
2612:evaluate investments in projects
2595:Stochastic modelling (insurance)
1773:in inputs and systems with many
1753:with Monte Carlo simulation and
1624:Monte Carlo simulation: Drawing
104:Generate inputs randomly from a
65:to solve problems that might be
9252:Least-squares spectral analysis
7048:Monte Carlo Statistical Methods
6653:Handbook of Monte Carlo Methods
6059:
6032:
5997:
5941:
5843:
5837:Handbook of Monte Carlo Methods
5784:
5759:
5730:
5712:
5671:
5630:
5593:
5575:
5532:
5506:
5477:
5450:
5405:
5394:
5367:
5303:
5260:
5226:Dietrich, S.; Boyd, I. (1996).
5219:
5210:
5199:
5188:
5153:
5142:
5100:Physics in Medicine and Biology
5091:
5049:Physics in Medicine and Biology
5040:
4996:Physics in Medicine and Biology
4983:
4900:
4889:
4685:
4644:
4558:
4548:
4538:
4528:
4518:
4508:
4443:
4364:
4321:
4240:
4003:Séminaire de Probabilités XXXIV
3935:
3917:
3890:
3864:
3805:
3668:
3633:
3589:Computer Physics Communications
3580:
3545:
3436:
3179:The Journal of Chemical Physics
3160:"Modeling Without Measurements"
2340:Bayesian inference in phylogeny
1919:Smoothed particle hydrodynamics
1764:
8233:Mean-unbiased minimum-variance
7336:
7204:. VDM Verlag Dr. Mueller e.K.
7200:Szirmay-Kalos, LĂĄszlĂł (2008).
7140:Sawilowsky, Shlomo S. (2003).
7125:. Rochester Hills, MI: JMASM.
7085:Savvides, Savvakis C. (1994).
6817:10.1080/01621459.1949.10483310
6678:Astrophysics and Space Science
6127:Mosegaard & Tarantola 1995
3350:
3323:
3301:10.1080/01621459.2000.10473908
3280:
3229:
3170:
3151:
3116:
2979:and GrĂŒne-Yanoff and Weirich.
2699:
2608:Monte Carlo methods in finance
2583:Monte Carlo methods in finance
2412:To provide implementations of
2164:
2157:that form the basis of modern
2131:binary collision approximation
2107:Monte Carlo molecular modeling
1648:Monte Carlo and random numbers
1574:
1398:Los Alamos National Laboratory
1275:
1272:
1269:
1255:
1246:
1235:
1220:
1207:
946:
936:
403:Suppose one wants to know the
258:, and generating draws from a
237:
232:pseudorandom number generators
1:
9546:Geographic information system
8762:Simultaneous equations models
6622:. Cambridge University Press.
6519:American Mathematical Society
5600:Silver, David; Veness, Joel.
5401:Sawilowsky & Fahoome 2003
4875:10.1080/00423114.2017.1283046
4804:10.1016/s0246-0203(00)01064-5
4581:Annals of Applied Probability
4062:10.1016/S0304-4149(99)00094-0
3395:Kolokoltsov, Vassili (2010).
3359:IEEE Control Systems Magazine
3332:IEEE Control Systems Magazine
3092:
3071:Multilevel Monte Carlo method
3016:Direct simulation Monte Carlo
2970:
2934:leads to the definition of a
2930:Probabilistic formulation of
2870:MetropolisâHastings algorithm
2844:recursive stratified sampling
2722:Errors reduce by a factor of
2239:direct simulation Monte Carlo
1914:Dissipative particle dynamics
1704:Pseudo-random number sampling
1579:There is no consensus on how
1516:diffusion Monte Carlo methods
667:| > 0. Choose the desired
536:
439:that is arbitrarily close to
431:exists. A sufficiently large
322:, integrals described by the
8729:Coefficient of determination
8340:Uniformly most powerful test
6485:10.1016/0019-1035(79)90199-4
6026:10.1016/0021-9991(87)90054-4
5879:10.1371/journal.pone.0189718
5794:Numerical Methods in Finance
5655:10.1007/978-3-642-17928-0_10
5195:MacGillivray & Dodd 1982
5182:10.1016/0168-583X(84)90321-5
4424:(4): 555â580. Archived from
3642:Chemical Engineering Science
3097:
3086:Temporal difference learning
2868:). Such methods include the
2320:probability density function
2260:that forms the heart of the
2187:microelectronics engineering
1502:Institute for Advanced Study
372:nonlinear filtering equation
278:interacting particle systems
7:
9683:Risk analysis methodologies
9298:Proportional hazards models
9242:Spectral density estimation
9224:Vector autoregression (VAR)
8658:Maximum posterior estimator
7890:Randomized controlled trial
6954:10.1529/biophysj.107.125369
6753:Journal of Chemical Physics
6706:MacKeown, P. Kevin (1997).
6514:Introduction to Probability
6496:. Reading: Addison-Wesley.
6438:10.1088/0031-9155/55/17/021
5812:10.1007/978-3-642-25746-9_1
5559:10.1007/978-3-540-87608-3_6
5120:10.1088/0031-9155/51/13/R17
5069:10.1088/0031-9155/59/6/R183
5016:10.1088/0031-9155/59/4/R151
4188:10.1103/physrevlett.71.2159
3046:Mean-field particle methods
3006:Auxiliary field Monte Carlo
2982:
2960:distribution is available.
2888:Simulation and optimization
2299:mean-field particle methods
2127:radiation materials science
1449:for the development of the
1417:, suggested using the name
1050:run the simulation for the
906:is sufficiently large when
772:run the simulation for the
566:throw the three dice until
487:run the simulation for the
92:
10:
9699:
9668:Statistical approximations
9058:Multivariate distributions
7478:Average absolute deviation
7015:Cambridge University Press
6173:
6116:http://www.jhuapl.edu/ISSO
5471:10.1016/j.csda.2009.09.018
5376:Journal of Urban Economics
5320:Cambridge University Press
4575:Del Moral, Pierre (1998).
4409:Del Moral, Pierre (1996).
4076:Del Moral, Pierre (2003).
3963:Del Moral, Pierre (2004).
3818:Proc. Natl. Acad. Sci. USA
3554:AIP Conference Proceedings
3419:Del Moral, Pierre (2013).
3401:Cambridge University Press
3397:Nonlinear Markov processes
3021:Dynamic Monte Carlo method
3011:Biology Monte Carlo method
2919:traveling salesman problem
2908:traveling salesman problem
2891:
2703:
2680:as a real instance of the
2580:
2516:
2456:
2220:quantitative risk analysis
2115:statistical field theories
2093:calculations to designing
2074:
1849:Morse/Long-range potential
1437:and others programmed the
1357:
135:quadrant (circular sector)
115:computation of the outputs
18:
9572:
9526:
9463:
9416:
9379:
9375:
9362:
9334:
9316:
9283:
9274:
9232:
9179:
9140:
9089:
9080:
9046:Structural equation model
9001:
8958:
8954:
8929:
8888:
8854:
8808:
8775:
8737:
8704:
8700:
8676:
8616:
8525:
8444:
8408:
8399:
8382:Score/Lagrange multiplier
8367:
8320:
8265:
8191:
8182:
7992:
7988:
7975:
7934:
7908:
7860:
7815:
7797:Sample size determination
7762:
7758:
7745:
7649:
7604:
7578:
7560:
7516:
7468:
7388:
7379:
7375:
7362:
7344:
7161:10.22237/jmasm/1051748460
7094:Project Appraisal Journal
6605:Hubbard, Douglas (2009).
6574:Hubbard, Douglas (2007).
6249:10.1007/s10910-008-9467-3
5388:10.1016/j.jue.2014.02.005
5362:Milik & Skolnick 1993
5289:10.1016/J.JCP.2020.110002
4913:The Astrophysical Journal
4842:Kalos & Whitlock 2008
4630:10.1137/s0036139996307371
3812:McKean, Henry P. (1966).
3697:10.1016/j.jcp.2018.01.029
3662:10.1016/j.ces.2013.08.008
3619:10.1016/j.cpc.2014.01.006
3111:Kalos & Whitlock 2008
2878:Wang and Landau algorithm
2859:low-discrepancy sequences
1719:quasi-Monte Carlo methods
1714:Low-discrepancy sequences
753:is the mean of the first
435:will produce a value for
36:with a Monte Carlo method
9541:Environmental statistics
9063:Elliptical distributions
8856:Generalized linear model
8785:Simple linear regression
8555:HodgesâLehmann estimator
8012:Probability distribution
7921:Stochastic approximation
7483:Coefficient of variation
6993:10.1504/IJVD.2001.001963
6381:Eckhardt, Roger (1987).
5839:. John Wiley & Sons.
4944:10.3847/1538-4357/aa7ede
4342:10.1049/ip-f-2.1993.0015
4234:10.1103/PhysRevA.30.2713
4138:10.1103/physreve.61.4566
3911:10.1093/mind/LIX.236.433
3371:10.1109/MCS.2018.2876959
3344:10.1109/MCS.2003.1188770
3076:Quasi-Monte Carlo method
2936:probability distribution
2866:Markov chain Monte Carlo
2855:quasi-Monte Carlo method
2853:A similar approach, the
2694:Random number generation
2666:
2571:probability distribution
2422:asymptotic distributions
2250:Monte Carlo localization
2125:for quantum systems. In
1750:probability distribution
1708:probability distribution
1601:distinguishes between a
1514:, and more specifically
570:is met or first exceeded
346:model with a prescribed
340:Markov chain Monte Carlo
336:probability distribution
260:probability distribution
133:For example, consider a
106:probability distribution
19:Not to be confused with
9201:Cross-correlation (XCF)
8809:Non-standard predictors
8243:LehmannâScheffĂ© theorem
7916:Adaptive clinical trial
7272:. ACMO Academic Press.
6549:Hartmann, A.K. (2009).
6397:Fishman, G. S. (1995).
6264:Berg, Bernd A. (2004).
5436:10.1198/106186005X78800
4855:Vehicle System Dynamics
4603:10.1214/aoap/1028903535
2894:Stochastic optimization
2796:, this method displays
2771:curse of dimensionality
2706:Monte Carlo integration
2465:Monte-Carlo tree search
2459:Monte Carlo tree search
2276:reliability engineering
1854:Lennard-Jones potential
1608:Here are the examples:
1595:Monte Carlo integration
1571:Guionnet and L. Miclo.
1379:Buffon's needle problem
1348:embarrassingly parallel
776:time, producing result
368:McKeanâVlasov processes
286:kinetic models of gases
282:McKeanâVlasov processes
47:, are a broad class of
45:Monte Carlo experiments
32:The approximation of a
9597:Mathematics portal
9418:Engineering statistics
9326:NelsonâAalen estimator
8903:Analysis of covariance
8790:Ordinary least squares
8714:Pearson product-moment
8118:Statistical functional
8029:Empirical distribution
7862:Controlled experiments
7591:Frequency distribution
7369:Descriptive statistics
7225:Inverse Problem Theory
7032:Ripley, B. D. (1987).
6854:10.1002/prot.340150104
6710:. New York: Springer.
6401:. New York: Springer.
6366:. New York: Springer.
6290:. New York: Springer.
6220:10.1515/mcma-2016-0102
6114:, Wiley, Hoboken, NJ.
5969:10.21315/km2021.39.2.8
5920:State Bar of Wisconsin
5253:10.1006/jcph.1996.0141
4761:C. R. Acad. Sci. Paris
3839:10.1073/pnas.56.6.1907
3258:10.1093/biomet/57.1.97
2900:numerical optimization
2882:sequential Monte Carlo
2824:
2757:
2750:
2715:
2621:
2599:Stochastic asset model
2237:fluid flows using the
2091:quantum chromodynamics
1642:Gelman-Rubin statistic
1630:Monte Carlo simulation
1544:Sequential Monte Carlo
1533:Marshall N. Rosenbluth
1421:, which refers to the
1411:
1297:
959:
580:= the number of throws
130:
37:
9678:Randomized algorithms
9673:Stochastic simulation
9658:Computational physics
9653:Statistical mechanics
9513:Population statistics
9455:System identification
9189:Autocorrelation (ACF)
9117:Exponential smoothing
9031:Discriminant analysis
9026:Canonical correlation
8890:Partition of variance
8752:Regression validation
8596:(JonckheereâTerpstra)
8495:Likelihood-ratio test
8184:Frequentist inference
8096:Locationâscale family
8017:Sampling distribution
7982:Statistical inference
7949:Cross-sectional study
7936:Observational studies
7895:Randomized experiment
7724:Stem-and-leaf display
7526:Central limit theorem
7249:John Wiley & Sons
7034:Stochastic Simulation
6658:John Wiley & Sons
6611:John Wiley & Sons
6584:John Wiley & Sons
6569:on February 11, 2009.
6337:10.1145/143242.143290
6110:Spall, J. C. (2003),
5493:Sander.landofsand.com
5322:. 2013. p. 697.
4711:10.1007/s004400050249
4670:10.1007/s004400050131
3943:Barricelli, Nils Aall
3925:Barricelli, Nils Aall
3495:Owen, Art B. (2013).
3425:. Chapman & Hall/
2825:
2794:central limit theorem
2762:numerical integration
2751:
2721:
2713:
2672:Nassim Nicholas Taleb
2544:, computer generated
2336:computational biology
2330:Computational biology
2231:rarefied gas dynamics
2083:computational physics
1789:Computational physics
1674:uniformly distributed
1586:stochastic simulation
1537:Arianna W. Rosenbluth
1506:Princeton, New Jersey
1402:
1298:
960:
256:numerical integration
125:
118:Aggregate the results
31:
21:Monte Carlo algorithm
9436:Probabilistic design
9021:Principal components
8864:Exponential families
8816:Nonlinear regression
8795:General linear model
8757:Mixed effects models
8747:Errors and residuals
8724:Confounding variable
8626:Bayesian probability
8604:Van der Waerden test
8594:Ordered alternative
8359:Multiple comparisons
8238:RaoâBlackwellization
8201:Estimating equations
8157:Statistical distance
7875:Factorial experiment
7408:Arithmetic-Geometric
7303:at Wikimedia Commons
7243:Vose, David (2008).
6555:. World Scientific.
6321:. pp. 123â129.
6182:Anderson, Herbert L.
5520:on November 29, 2015
4496:on November 10, 2022
4155:on November 7, 2014.
3772:10.1109/MAHC.2014.40
2949:marginal probability
2800:
2726:
2677:Fooled by Randomness
2577:Finance and business
2171:sensitivity analysis
1954:Metropolis algorithm
1655:truly random numbers
1612:Simulation: Drawing
1498:Nils Aall Barricelli
1195:
1185:/2, use a value for
1054:time, giving result
912:
491:time, giving result
320:law of large numbers
274:cellular Potts model
173:a quadrant within it
169:Draw a square, then
9663:Sampling techniques
9643:Monte Carlo methods
9508:Official statistics
9431:Methods engineering
9112:Seasonal adjustment
8880:Poisson regressions
8800:Bayesian regression
8739:Regression analysis
8719:Partial correlation
8691:Regression analysis
8290:Prediction interval
8285:Likelihood interval
8275:Confidence interval
8267:Interval estimation
8228:Unbiased estimators
8046:Model specification
7926:Up-and-down designs
7614:Partial correlation
7570:Index of dispersion
7488:Interquartile range
7106:10.2139/ssrn.265905
6946:2009BpJ....96.1076O
6898:1995JGR...10012431M
6892:(B7): 12431â12447.
6765:1953JChPh..21.1087M
6629:Monte Carlo Methods
6534:. London: Methuen.
6532:Monte Carlo Methods
6477:1979Icar...38..451G
6430:2010PMB....55.5213F
6018:1987JCoPh..68..237M
5929:on November 6, 2018
5870:2017PLoSO..1289718A
5647:2011LNCS.6515..105L
5639:Computers and Games
5541:Computers and Games
5281:2021JCoPh.42910002C
5244:1996JCoPh.126..328D
5174:1984NIMPB...2..814M
5112:2006PMB....51R.287R
5061:2014PMB....59R.183H
5008:2014PMB....59R.151J
4935:2017ApJ...845...66R
4867:2017VSD....55..827S
4796:2001AIHPB..37..155D
4471:1997ITAES..33..835C
4297:1955JChPh..23..356R
4226:1984PhRvA..30.2713H
4220:(2713): 2713â2719.
4180:1993PhRvL..71.2159C
4130:2000PhRvE..61.4566A
3830:1966PNAS...56.1907M
3689:2018JCoPh.360...93L
3654:2013ChEnS.104..451W
3611:2014CoPhC.185.1355C
3566:2016AIPC.1773g0001A
3250:1970Bimka..57...97H
3191:1953JChPh..21.1087M
3036:Kinetic Monte Carlo
2840:stratified sampling
2835:importance sampling
2682:reverse Turing test
2530:global illumination
2399:Cauchy distribution
2356:thought experiments
2246:autonomous robotics
2198:integrated circuits
2159:weather forecasting
2119:Quantum Monte Carlo
2103:statistical physics
1937:Monte Carlo methods
1593:being reserved for
1512:Quantum Monte Carlo
1478:Henry P. McKean Jr.
1463:operations research
1435:Nicholas Metropolis
1415:Nicholas Metropolis
1392:In the late 1940s,
1372:simulated annealing
1341:Computational costs
1102:Choose a value for
896:is the mean of the
380:mean-field particle
305:boundary conditions
41:Monte Carlo methods
34:normal distribution
9648:Numerical analysis
9528:Spatial statistics
9408:Medical statistics
9308:First hitting time
9262:Whittle likelihood
8913:Degrees of freedom
8908:Multivariate ANOVA
8841:Heteroscedasticity
8653:Bayesian estimator
8618:Bayesian inference
8467:KolmogorovâSmirnov
8352:Randomization test
8322:Testing hypotheses
8295:Tolerance interval
8206:Maximum likelihood
8101:Exponential family
8034:Density estimation
7994:Statistical theory
7954:Natural experiment
7900:Scientific control
7817:Survey methodology
7503:Standard deviation
7301:Monte Carlo method
6737:Los Alamos Science
6691:10.1007/BF00683346
6390:Los Alamos Science
6194:Los Alamos Science
5726:. January 3, 2014.
5707:Szirmay-Kalos 2008
4095:10.1051/ps:2003001
4012:10.1007/BFb0103798
3031:Genetic algorithms
2997:Mathematics portal
2820:
2819:
2758:
2746:
2745:
2716:
2688:Use in mathematics
2610:are often used to
2524:Design and visuals
2444:randomization test
2436:Fisher information
2429:Bayesian inference
2377:Applied statistics
2371:rendering equation
2338:, for example for
2303:empirical measures
2287:Bayesian inference
2269:telecommunications
2218:and contribute to
2213:mineral processing
2121:methods solve the
2111:molecular dynamics
2087:physical chemistry
1982:Molecular dynamics
1552:Bayesian inference
1482:Theodore E. Harris
1459:physical chemistry
1423:Monte Carlo Casino
1352:parallel computing
1293:
955:
399:Simple Monte Carlo
376:empirical measures
356:empirical measures
301:definite integrals
270:degrees of freedom
131:
71:Monte Carlo Casino
38:
9630:
9629:
9568:
9567:
9564:
9563:
9503:National accounts
9473:Actuarial science
9465:Social statistics
9358:
9357:
9354:
9353:
9350:
9349:
9285:Survival function
9270:
9269:
9132:Granger causality
8973:Contingency table
8948:Survival analysis
8925:
8924:
8921:
8920:
8777:Linear regression
8672:
8671:
8668:
8667:
8643:Credible interval
8612:
8611:
8395:
8394:
8211:Method of moments
8080:Parametric family
8041:Statistical model
7971:
7970:
7967:
7966:
7885:Random assignment
7807:Statistical power
7741:
7740:
7737:
7736:
7586:Contingency table
7556:
7555:
7423:Generalized/power
7299:Media related to
7279:978-619-90684-3-4
7235:978-0-89871-572-9
7220:Tarantola, Albert
7211:978-3-8364-7919-6
7132:978-0-9740236-0-1
7077:978-0-470-17793-8
7058:978-0-387-21239-5
7024:978-0-521-43064-7
6915:on March 10, 2021
6906:10.1029/94JB03097
6773:10.1063/1.1699114
6717:978-981-3083-26-4
6667:978-0-470-17793-8
6642:978-3-527-40760-6
6562:978-981-283-415-7
6541:978-0-416-52340-9
6503:978-0-201-16504-3
6424:(17): 5213â5229.
6408:978-0-387-94527-9
6373:978-0-387-95146-1
6346:978-0-89791-489-5
6297:978-0-387-54369-7
6275:978-981-238-935-0
6053:10.1021/jp972280j
5993:Press et al. 1996
5821:978-3-642-25745-2
5664:978-3-642-17927-3
5568:978-3-540-87607-6
5350:Ojeda et al. 2009
5329:978-1-107-66182-0
5106:(13): R287âR301.
4306:10.1063/1.1741967
4021:978-3-540-67314-9
3574:10.1063/1.4964983
3199:10.1063/1.1699114
3137:10.1002/wics.1314
3125:WIREs Comput Stat
2817:
2783:degree of freedom
2775:iterated integral
2743:
2616:project schedules
2566:search and rescue
2552:Search and rescue
2418:permutation tests
2362:Computer graphics
2352:chemical reaction
2324:radiative forcing
2283:signal processing
2173:and quantitative
2123:many-body problem
2073:
2072:
1924:Turbulence models
1904:Lattice Boltzmann
1884:Finite difference
1781:Physical sciences
1659:primality testing
1548:signal processing
1091:
1061:
1048:
886:
866:
847:
836:
821:
810:
784:
770:
758:
743:
675:is indeed within
623:is large enough,
616:
599:
581:
571:
533:
519:
498:
303:with complicated
212:approximation of
9690:
9618:
9617:
9606:
9605:
9595:
9594:
9580:
9579:
9483:Crime statistics
9377:
9376:
9364:
9363:
9281:
9280:
9247:Fourier analysis
9234:Frequency domain
9214:
9161:
9127:Structural break
9087:
9086:
9036:Cluster analysis
8983:Log-linear model
8956:
8955:
8931:
8930:
8872:
8846:Homoscedasticity
8702:
8701:
8678:
8677:
8597:
8589:
8581:
8580:(KruskalâWallis)
8565:
8550:
8505:Cross validation
8490:
8472:AndersonâDarling
8419:
8406:
8405:
8377:Likelihood-ratio
8369:Parametric tests
8347:Permutation test
8330:1- & 2-tails
8221:Minimum distance
8193:Point estimation
8189:
8188:
8140:Optimal decision
8091:
7990:
7989:
7977:
7976:
7959:Quasi-experiment
7909:Adaptive designs
7760:
7759:
7747:
7746:
7624:Rank correlation
7386:
7385:
7377:
7376:
7364:
7363:
7331:
7324:
7317:
7308:
7307:
7298:
7283:
7262:
7247:(3rd ed.).
7239:
7215:
7196:
7194:
7192:
7186:
7175:
7165:
7163:
7136:
7117:
7091:
7081:
7062:
7041:
7038:Wiley & Sons
7028:
7005:
6996:
6987:(1â4): 183â194.
6975:
6965:
6940:(3): 1076â1082.
6924:
6922:
6920:
6914:
6908:. Archived from
6883:
6873:
6836:
6811:(247): 335â341.
6792:
6740:
6734:
6721:
6702:
6671:
6646:
6623:
6614:
6601:
6581:
6570:
6565:. Archived from
6545:
6526:
6507:
6488:
6457:
6412:
6393:
6387:
6377:
6358:
6330:
6313:
6301:
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6158:
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6140:
6135:
6129:
6124:
6118:
6108:
6102:
6101:
6083:
6081:cond-mat/0212648
6063:
6057:
6056:
6036:
6030:
6029:
6001:
5995:
5990:
5981:
5980:
5954:
5945:
5939:
5938:
5936:
5934:
5928:
5922:. Archived from
5917:
5908:
5902:
5901:
5891:
5881:
5864:(12): e0189718.
5847:
5841:
5840:
5832:
5826:
5825:
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5782:
5781:
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5777:
5763:
5757:
5756:
5754:
5752:
5743:
5734:
5728:
5727:
5716:
5710:
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5698:
5697:
5695:
5693:
5684:
5675:
5669:
5668:
5634:
5628:
5627:
5625:
5623:
5618:on July 18, 2016
5617:
5611:. Archived from
5606:
5597:
5591:
5590:
5588:
5579:
5573:
5572:
5552:
5536:
5530:
5529:
5527:
5525:
5516:. Archived from
5510:
5504:
5503:
5501:
5499:
5490:
5481:
5475:
5474:
5454:
5448:
5447:
5429:
5409:
5403:
5398:
5392:
5391:
5371:
5365:
5359:
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5341:
5340:
5338:
5336:
5317:
5307:
5301:
5300:
5264:
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5257:
5255:
5223:
5217:
5214:
5208:
5203:
5197:
5192:
5186:
5185:
5157:
5151:
5146:
5140:
5139:
5095:
5089:
5088:
5055:(6): R183âR231.
5044:
5038:
5037:
5027:
5002:(4): R151âR182.
4987:
4981:
4975:
4969:
4963:
4957:
4956:
4946:
4928:
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4898:
4893:
4887:
4886:
4850:
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4839:
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4808:
4807:
4775:
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4749:
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4730:
4724:
4723:
4713:
4689:
4683:
4682:
4672:
4648:
4642:
4641:
4624:(5): 1568â1590.
4613:
4607:
4606:
4596:
4572:
4566:
4562:
4556:
4552:
4546:
4542:
4536:
4532:
4526:
4522:
4516:
4512:
4506:
4505:
4503:
4501:
4495:
4489:. Archived from
4479:10.1109/7.599254
4456:
4447:
4441:
4440:
4438:
4436:
4431:on March 4, 2016
4430:
4415:
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4396:
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4362:
4361:
4325:
4319:
4318:
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4266:
4253:
4244:
4238:
4237:
4209:
4200:
4199:
4163:
4157:
4156:
4154:
4148:. Archived from
4124:(4): 4566â4575.
4115:
4106:
4100:
4099:
4097:
4073:
4067:
4066:
4064:
4040:
4034:
4033:
3993:
3984:
3983:
3960:
3951:
3950:
3939:
3933:
3932:
3921:
3915:
3914:
3905:(238): 433â460.
3894:
3888:
3887:
3877:
3868:
3862:
3861:
3851:
3841:
3824:(6): 1907â1911.
3809:
3803:
3802:
3790:
3784:
3783:
3751:
3745:
3739:
3730:
3724:
3718:
3712:
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3665:
3637:
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3630:
3604:
3595:(5): 1355â1363.
3584:
3578:
3577:
3549:
3543:
3542:
3534:
3528:
3527:
3515:
3506:
3505:
3503:
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3479:
3478:
3460:
3458:cond-mat/0212648
3440:
3434:
3433:
3416:
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3404:
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3383:
3382:
3354:
3348:
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3320:
3295:(449): 121â134.
3284:
3278:
3277:
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3185:(6): 1087â1092.
3174:
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2994:
2993:
2943:defined, etc.).
2932:inverse problems
2926:Inverse problems
2829:
2827:
2826:
2821:
2818:
2813:
2811:
2755:
2753:
2752:
2747:
2744:
2739:
2737:
2640:physical assault
2414:hypothesis tests
2291:particle filters
2229:, in particular
2139:particle physics
2135:ion implantation
2065:
2058:
2051:
1977:Particle-in-cell
1899:Boundary element
1859:Yukawa potential
1822:Particle physics
1812:Electromagnetics
1799:
1785:
1784:
1730:Mersenne Twister
1528:Robert Richtmyer
1467:Rand Corporation
1407:John von Neumann
1384:
1305:For example, if
1302:
1300:
1299:
1294:
1292:
1291:
1282:
1265:
1245:
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669:confidence level
600:
583:
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548:
520:
500:
469:
414:(and knows that
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202:
200:
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196:
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9689:
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9626:
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9560:
9522:
9459:
9445:quality control
9412:
9394:Clinical trials
9371:
9346:
9330:
9318:Hazard function
9312:
9266:
9228:
9212:
9175:
9171:BreuschâGodfrey
9159:
9136:
9076:
9051:Factor analysis
8997:
8978:Graphical model
8950:
8917:
8884:
8870:
8850:
8804:
8771:
8733:
8696:
8695:
8664:
8608:
8595:
8587:
8579:
8563:
8548:
8527:Rank statistics
8521:
8500:Model selection
8488:
8446:Goodness of fit
8440:
8417:
8391:
8363:
8316:
8261:
8250:Median unbiased
8178:
8089:
8022:Order statistic
7984:
7963:
7930:
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7856:
7811:
7754:
7752:Data collection
7733:
7645:
7600:
7574:
7552:
7512:
7464:
7381:Continuous data
7371:
7358:
7340:
7335:
7291:
7286:
7280:
7259:
7236:
7212:
7190:
7188:
7187:on May 25, 2012
7184:
7173:
7133:
7089:
7078:
7059:
7025:
6918:
6916:
6912:
6886:J. Geophys. Res
6881:
6732:
6718:
6668:
6660:. p. 772.
6643:
6598:
6563:
6542:
6504:
6418:Phys. Med. Biol
6409:
6385:
6374:
6347:
6306:Caflisch, R. E.
6298:
6276:
6188:
6176:
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6170:
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5957:Kajian Malaysia
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5932:
5930:
5926:
5915:
5909:
5905:
5848:
5844:
5833:
5829:
5822:
5803:10.1.1.359.7957
5789:
5785:
5775:
5773:
5765:
5764:
5760:
5750:
5748:
5741:
5735:
5731:
5718:
5717:
5713:
5705:
5701:
5691:
5689:
5682:
5676:
5672:
5665:
5635:
5631:
5621:
5619:
5615:
5604:
5598:
5594:
5586:
5580:
5576:
5569:
5550:10.1.1.159.4373
5537:
5533:
5523:
5521:
5512:
5511:
5507:
5497:
5495:
5488:
5482:
5478:
5455:
5451:
5410:
5406:
5399:
5395:
5372:
5368:
5360:
5356:
5348:
5344:
5334:
5332:
5330:
5315:
5309:
5308:
5304:
5265:
5261:
5224:
5220:
5215:
5211:
5204:
5200:
5193:
5189:
5158:
5154:
5147:
5143:
5096:
5092:
5045:
5041:
4988:
4984:
4976:
4972:
4964:
4960:
4905:
4901:
4894:
4890:
4851:
4847:
4840:
4836:
4831:Sawilowsky 2003
4829:
4822:
4815:
4811:
4776:
4772:
4757:
4753:
4737:
4731:
4727:
4690:
4686:
4649:
4645:
4614:
4610:
4573:
4569:
4563:
4559:
4553:
4549:
4543:
4539:
4533:
4529:
4523:
4519:
4513:
4509:
4499:
4497:
4493:
4454:
4448:
4444:
4434:
4432:
4428:
4413:
4407:
4400:
4385:10.2307/1390750
4369:
4365:
4326:
4322:
4277:
4270:
4251:
4245:
4241:
4210:
4203:
4168:Phys. Rev. Lett
4164:
4160:
4152:
4113:
4107:
4103:
4074:
4070:
4041:
4037:
4022:
3994:
3987:
3977:
3961:
3954:
3940:
3936:
3922:
3918:
3895:
3891:
3875:
3869:
3865:
3810:
3806:
3791:
3787:
3752:
3748:
3740:
3733:
3725:
3721:
3715:Metropolis 1987
3713:
3704:
3673:
3669:
3638:
3634:
3585:
3581:
3550:
3546:
3535:
3531:
3516:
3509:
3501:
3493:
3482:
3441:
3437:
3429:. p. 626.
3417:
3408:
3393:
3386:
3355:
3351:
3328:
3324:
3285:
3281:
3234:
3230:
3175:
3171:
3156:
3152:
3121:
3117:
3109:
3105:
3100:
3095:
3090:
2995:
2988:
2985:
2973:
2928:
2896:
2890:
2848:VEGAS algorithm
2812:
2807:
2801:
2798:
2797:
2738:
2733:
2727:
2724:
2723:
2708:
2702:
2690:
2669:
2648:
2646:Library science
2624:
2601:
2579:
2554:
2526:
2521:
2461:
2455:
2379:
2364:
2350:to see if some
2332:
2312:
2297:are a class of
2258:particle filter
2167:
2155:ensemble models
2133:for simulating
2079:
2069:
2040:
2039:
1995:
1987:
1986:
1967:
1959:
1958:
1939:
1929:
1928:
1879:
1869:
1868:
1864:Morse potential
1844:
1834:
1783:
1767:
1742:
1650:
1577:
1382:
1360:
1343:
1287:
1283:
1278:
1261:
1241:
1223:
1219:
1196:
1193:
1192:
1155:
1144:
1137:
1131:
1124:
1097:
1092:
1076:
1059:
1033:
991:
980:
949:
945:
931:
925:
921:
913:
910:
909:
894:
887:
879:
863:
846:
842:
833:
820:
816:
808:
804:
797:
790:
781:
751:
742:
735:
728:
720:
683:. Let z be the
653:
651:General formula
648:
627:will be within
617:
596:
578:
539:
534:
513:
496:
401:
352:ergodic theorem
309:oil exploration
240:
213:
204:
197:
194:
190:
189:
188:
186:
161:
159:, the value of
153:
150:
146:
145:
144:
142:
137:inscribed in a
127:
108:over the domain
95:
59:random sampling
24:
17:
12:
11:
5:
9696:
9686:
9685:
9680:
9675:
9670:
9665:
9660:
9655:
9650:
9645:
9628:
9627:
9625:
9624:
9612:
9600:
9586:
9573:
9570:
9569:
9566:
9565:
9562:
9561:
9559:
9558:
9553:
9548:
9543:
9538:
9532:
9530:
9524:
9523:
9521:
9520:
9515:
9510:
9505:
9500:
9495:
9490:
9485:
9480:
9475:
9469:
9467:
9461:
9460:
9458:
9457:
9452:
9447:
9438:
9433:
9428:
9422:
9420:
9414:
9413:
9411:
9410:
9405:
9400:
9391:
9389:Bioinformatics
9385:
9383:
9373:
9372:
9360:
9359:
9356:
9355:
9352:
9351:
9348:
9347:
9345:
9344:
9338:
9336:
9332:
9331:
9329:
9328:
9322:
9320:
9314:
9313:
9311:
9310:
9305:
9300:
9295:
9289:
9287:
9278:
9272:
9271:
9268:
9267:
9265:
9264:
9259:
9254:
9249:
9244:
9238:
9236:
9230:
9229:
9227:
9226:
9221:
9216:
9208:
9203:
9198:
9197:
9196:
9194:partial (PACF)
9185:
9183:
9177:
9176:
9174:
9173:
9168:
9163:
9155:
9150:
9144:
9142:
9141:Specific tests
9138:
9137:
9135:
9134:
9129:
9124:
9119:
9114:
9109:
9104:
9099:
9093:
9091:
9084:
9078:
9077:
9075:
9074:
9073:
9072:
9071:
9070:
9055:
9054:
9053:
9043:
9041:Classification
9038:
9033:
9028:
9023:
9018:
9013:
9007:
9005:
8999:
8998:
8996:
8995:
8990:
8988:McNemar's test
8985:
8980:
8975:
8970:
8964:
8962:
8952:
8951:
8927:
8926:
8923:
8922:
8919:
8918:
8916:
8915:
8910:
8905:
8900:
8894:
8892:
8886:
8885:
8883:
8882:
8866:
8860:
8858:
8852:
8851:
8849:
8848:
8843:
8838:
8833:
8828:
8826:Semiparametric
8823:
8818:
8812:
8810:
8806:
8805:
8803:
8802:
8797:
8792:
8787:
8781:
8779:
8773:
8772:
8770:
8769:
8764:
8759:
8754:
8749:
8743:
8741:
8735:
8734:
8732:
8731:
8726:
8721:
8716:
8710:
8708:
8698:
8697:
8694:
8693:
8688:
8682:
8674:
8673:
8670:
8669:
8666:
8665:
8663:
8662:
8661:
8660:
8650:
8645:
8640:
8639:
8638:
8633:
8622:
8620:
8614:
8613:
8610:
8609:
8607:
8606:
8601:
8600:
8599:
8591:
8583:
8567:
8564:(MannâWhitney)
8559:
8558:
8557:
8544:
8543:
8542:
8531:
8529:
8523:
8522:
8520:
8519:
8518:
8517:
8512:
8507:
8497:
8492:
8489:(ShapiroâWilk)
8484:
8479:
8474:
8469:
8464:
8456:
8450:
8448:
8442:
8441:
8439:
8438:
8430:
8421:
8409:
8403:
8401:Specific tests
8397:
8396:
8393:
8392:
8390:
8389:
8384:
8379:
8373:
8371:
8365:
8364:
8362:
8361:
8356:
8355:
8354:
8344:
8343:
8342:
8332:
8326:
8324:
8318:
8317:
8315:
8314:
8313:
8312:
8307:
8297:
8292:
8287:
8282:
8277:
8271:
8269:
8263:
8262:
8260:
8259:
8254:
8253:
8252:
8247:
8246:
8245:
8240:
8225:
8224:
8223:
8218:
8213:
8208:
8197:
8195:
8186:
8180:
8179:
8177:
8176:
8171:
8166:
8165:
8164:
8154:
8149:
8148:
8147:
8137:
8136:
8135:
8130:
8125:
8115:
8110:
8105:
8104:
8103:
8098:
8093:
8077:
8076:
8075:
8070:
8065:
8055:
8054:
8053:
8048:
8038:
8037:
8036:
8026:
8025:
8024:
8014:
8009:
8004:
7998:
7996:
7986:
7985:
7973:
7972:
7969:
7968:
7965:
7964:
7962:
7961:
7956:
7951:
7946:
7940:
7938:
7932:
7931:
7929:
7928:
7923:
7918:
7912:
7910:
7906:
7905:
7903:
7902:
7897:
7892:
7887:
7882:
7877:
7872:
7866:
7864:
7858:
7857:
7855:
7854:
7852:Standard error
7849:
7844:
7839:
7838:
7837:
7832:
7821:
7819:
7813:
7812:
7810:
7809:
7804:
7799:
7794:
7789:
7784:
7782:Optimal design
7779:
7774:
7768:
7766:
7756:
7755:
7743:
7742:
7739:
7738:
7735:
7734:
7732:
7731:
7726:
7721:
7716:
7711:
7706:
7701:
7696:
7691:
7686:
7681:
7676:
7671:
7666:
7661:
7655:
7653:
7647:
7646:
7644:
7643:
7638:
7637:
7636:
7631:
7621:
7616:
7610:
7608:
7602:
7601:
7599:
7598:
7593:
7588:
7582:
7580:
7579:Summary tables
7576:
7575:
7573:
7572:
7566:
7564:
7558:
7557:
7554:
7553:
7551:
7550:
7549:
7548:
7543:
7538:
7528:
7522:
7520:
7514:
7513:
7511:
7510:
7505:
7500:
7495:
7490:
7485:
7480:
7474:
7472:
7466:
7465:
7463:
7462:
7457:
7452:
7451:
7450:
7445:
7440:
7435:
7430:
7425:
7420:
7415:
7413:Contraharmonic
7410:
7405:
7394:
7392:
7383:
7373:
7372:
7360:
7359:
7357:
7356:
7351:
7345:
7342:
7341:
7334:
7333:
7326:
7319:
7311:
7305:
7304:
7290:
7289:External links
7287:
7285:
7284:
7278:
7263:
7257:
7240:
7234:
7216:
7210:
7197:
7166:
7154:(1): 218â225.
7137:
7131:
7118:
7082:
7076:
7063:
7057:
7042:
7029:
7023:
7006:
6997:
6976:
6925:
6874:
6837:
6797:Metropolis, N.
6793:
6745:Metropolis, N.
6741:
6726:Metropolis, N.
6722:
6716:
6703:
6685:(2): 419â435.
6672:
6666:
6647:
6641:
6624:
6615:
6602:
6596:
6571:
6561:
6546:
6540:
6527:
6508:
6502:
6489:
6471:(3): 451â455.
6458:
6413:
6407:
6394:
6392:(15): 131â137.
6378:
6372:
6359:
6345:
6328:10.1.1.43.9296
6314:
6302:
6296:
6280:
6274:
6261:
6243:(2): 363â426.
6232:
6203:
6177:
6175:
6172:
6169:
6168:
6159:
6150:
6141:
6138:Tarantola 2005
6130:
6119:
6103:
6074:(3): 411â436.
6058:
6047:(5): 865â880.
6031:
6012:(1): 237â248.
5996:
5982:
5963:(2): 179â202.
5940:
5903:
5842:
5827:
5820:
5783:
5771:risk.octigo.pl
5758:
5729:
5711:
5699:
5670:
5663:
5629:
5609:0.cs.ucl.ac.uk
5592:
5574:
5567:
5531:
5505:
5476:
5465:(2): 272â289.
5449:
5427:10.1.1.142.738
5420:(4): 889â909.
5404:
5393:
5366:
5354:
5342:
5328:
5302:
5259:
5218:
5209:
5198:
5187:
5168:(1): 814â818.
5152:
5141:
5090:
5039:
4982:
4970:
4958:
4899:
4896:Davenport 1992
4888:
4861:(6): 827â852.
4845:
4834:
4820:
4809:
4790:(2): 155â194.
4770:
4751:
4725:
4704:(4): 549â578.
4684:
4663:(2): 217â244.
4643:
4608:
4594:10.1.1.55.5257
4567:
4557:
4547:
4537:
4527:
4517:
4507:
4465:(3): 835â850.
4442:
4398:
4363:
4336:(2): 107â113.
4320:
4291:(2): 356â359.
4268:
4239:
4201:
4158:
4101:
4068:
4055:(2): 193â216.
4035:
4020:
3985:
3975:
3952:
3934:
3916:
3889:
3863:
3804:
3785:
3746:
3744:, p. 250.
3731:
3719:
3702:
3667:
3632:
3579:
3544:
3529:
3507:
3480:
3451:(3): 411â436.
3435:
3406:
3403:. p. 375.
3384:
3349:
3322:
3279:
3228:
3169:
3150:
3131:(6): 386â392.
3115:
3102:
3101:
3099:
3096:
3094:
3091:
3089:
3088:
3083:
3081:Sobol sequence
3078:
3073:
3068:
3063:
3058:
3053:
3048:
3043:
3038:
3033:
3028:
3023:
3018:
3013:
3008:
3002:
3001:
3000:
2984:
2981:
2972:
2969:
2927:
2924:
2904:computer chess
2892:Main article:
2889:
2886:
2874:Gibbs sampling
2816:
2810:
2806:
2760:Deterministic
2742:
2736:
2732:
2704:Main article:
2701:
2698:
2689:
2686:
2668:
2665:
2647:
2644:
2623:
2620:
2578:
2575:
2558:US Coast Guard
2553:
2550:
2525:
2522:
2489:
2488:
2485:
2482:
2479:
2457:Main article:
2454:
2451:
2440:
2439:
2432:
2425:
2410:
2378:
2375:
2363:
2360:
2331:
2328:
2311:
2308:
2307:
2306:
2279:
2272:
2265:
2242:
2235:Knudsen number
2227:fluid dynamics
2223:
2201:
2179:process design
2166:
2163:
2071:
2070:
2068:
2067:
2060:
2053:
2045:
2042:
2041:
2038:
2037:
2032:
2027:
2022:
2017:
2012:
2007:
2002:
1996:
1993:
1992:
1989:
1988:
1985:
1984:
1979:
1974:
1968:
1965:
1964:
1961:
1960:
1957:
1956:
1951:
1949:Gibbs sampling
1946:
1940:
1935:
1934:
1931:
1930:
1927:
1926:
1921:
1916:
1911:
1909:Riemann solver
1906:
1901:
1896:
1894:Finite element
1891:
1886:
1880:
1877:Fluid dynamics
1875:
1874:
1871:
1870:
1867:
1866:
1861:
1856:
1851:
1845:
1842:
1841:
1838:
1837:
1836:
1835:
1829:
1827:Thermodynamics
1824:
1819:
1814:
1809:
1801:
1800:
1792:
1791:
1782:
1779:
1766:
1763:
1741:
1738:
1701:
1700:
1697:
1694:
1691:
1688:
1685:
1649:
1646:
1634:
1633:
1626:a large number
1622:
1618:
1576:
1573:
1471:U.S. Air Force
1443:fission weapon
1394:Stanislaw Ulam
1368:metaheuristics
1359:
1356:
1342:
1339:
1290:
1286:
1281:
1277:
1274:
1271:
1268:
1264:
1260:
1257:
1254:
1251:
1248:
1244:
1240:
1237:
1234:
1231:
1226:
1222:
1218:
1215:
1212:
1209:
1206:
1203:
1200:
1153:
1142:
1135:
1129:
1122:
1096:
1093:
1074:
1057:
1031:
1023:
989:
978:
952:
948:
944:
941:
938:
934:
928:
924:
920:
917:
892:
877:
861:
844:
840:
831:
818:
814:
806:
802:
795:
788:
779:
749:
740:
733:
726:
718:
714:
652:
649:
647:
641:
594:
576:
547:
538:
535:
511:
494:
468:
405:expected value
400:
397:
364:Markov process
328:empirical mean
324:expected value
239:
236:
228:
227:
224:
209:
208:
183:
180:
174:
120:
119:
116:
109:
102:
94:
91:
75:Stanislaw Ulam
15:
9:
6:
4:
3:
2:
9695:
9684:
9681:
9679:
9676:
9674:
9671:
9669:
9666:
9664:
9661:
9659:
9656:
9654:
9651:
9649:
9646:
9644:
9641:
9640:
9638:
9623:
9622:
9613:
9611:
9610:
9601:
9599:
9598:
9593:
9587:
9585:
9584:
9575:
9574:
9571:
9557:
9554:
9552:
9551:Geostatistics
9549:
9547:
9544:
9542:
9539:
9537:
9534:
9533:
9531:
9529:
9525:
9519:
9518:Psychometrics
9516:
9514:
9511:
9509:
9506:
9504:
9501:
9499:
9496:
9494:
9491:
9489:
9486:
9484:
9481:
9479:
9476:
9474:
9471:
9470:
9468:
9466:
9462:
9456:
9453:
9451:
9448:
9446:
9442:
9439:
9437:
9434:
9432:
9429:
9427:
9424:
9423:
9421:
9419:
9415:
9409:
9406:
9404:
9401:
9399:
9395:
9392:
9390:
9387:
9386:
9384:
9382:
9381:Biostatistics
9378:
9374:
9370:
9365:
9361:
9343:
9342:Log-rank test
9340:
9339:
9337:
9333:
9327:
9324:
9323:
9321:
9319:
9315:
9309:
9306:
9304:
9301:
9299:
9296:
9294:
9291:
9290:
9288:
9286:
9282:
9279:
9277:
9273:
9263:
9260:
9258:
9255:
9253:
9250:
9248:
9245:
9243:
9240:
9239:
9237:
9235:
9231:
9225:
9222:
9220:
9217:
9215:
9213:(BoxâJenkins)
9209:
9207:
9204:
9202:
9199:
9195:
9192:
9191:
9190:
9187:
9186:
9184:
9182:
9178:
9172:
9169:
9167:
9166:DurbinâWatson
9164:
9162:
9156:
9154:
9151:
9149:
9148:DickeyâFuller
9146:
9145:
9143:
9139:
9133:
9130:
9128:
9125:
9123:
9122:Cointegration
9120:
9118:
9115:
9113:
9110:
9108:
9105:
9103:
9100:
9098:
9097:Decomposition
9095:
9094:
9092:
9088:
9085:
9083:
9079:
9069:
9066:
9065:
9064:
9061:
9060:
9059:
9056:
9052:
9049:
9048:
9047:
9044:
9042:
9039:
9037:
9034:
9032:
9029:
9027:
9024:
9022:
9019:
9017:
9014:
9012:
9009:
9008:
9006:
9004:
9000:
8994:
8991:
8989:
8986:
8984:
8981:
8979:
8976:
8974:
8971:
8969:
8968:Cohen's kappa
8966:
8965:
8963:
8961:
8957:
8953:
8949:
8945:
8941:
8937:
8932:
8928:
8914:
8911:
8909:
8906:
8904:
8901:
8899:
8896:
8895:
8893:
8891:
8887:
8881:
8877:
8873:
8867:
8865:
8862:
8861:
8859:
8857:
8853:
8847:
8844:
8842:
8839:
8837:
8834:
8832:
8829:
8827:
8824:
8822:
8821:Nonparametric
8819:
8817:
8814:
8813:
8811:
8807:
8801:
8798:
8796:
8793:
8791:
8788:
8786:
8783:
8782:
8780:
8778:
8774:
8768:
8765:
8763:
8760:
8758:
8755:
8753:
8750:
8748:
8745:
8744:
8742:
8740:
8736:
8730:
8727:
8725:
8722:
8720:
8717:
8715:
8712:
8711:
8709:
8707:
8703:
8699:
8692:
8689:
8687:
8684:
8683:
8679:
8675:
8659:
8656:
8655:
8654:
8651:
8649:
8646:
8644:
8641:
8637:
8634:
8632:
8629:
8628:
8627:
8624:
8623:
8621:
8619:
8615:
8605:
8602:
8598:
8592:
8590:
8584:
8582:
8576:
8575:
8574:
8571:
8570:Nonparametric
8568:
8566:
8560:
8556:
8553:
8552:
8551:
8545:
8541:
8540:Sample median
8538:
8537:
8536:
8533:
8532:
8530:
8528:
8524:
8516:
8513:
8511:
8508:
8506:
8503:
8502:
8501:
8498:
8496:
8493:
8491:
8485:
8483:
8480:
8478:
8475:
8473:
8470:
8468:
8465:
8463:
8461:
8457:
8455:
8452:
8451:
8449:
8447:
8443:
8437:
8435:
8431:
8429:
8427:
8422:
8420:
8415:
8411:
8410:
8407:
8404:
8402:
8398:
8388:
8385:
8383:
8380:
8378:
8375:
8374:
8372:
8370:
8366:
8360:
8357:
8353:
8350:
8349:
8348:
8345:
8341:
8338:
8337:
8336:
8333:
8331:
8328:
8327:
8325:
8323:
8319:
8311:
8308:
8306:
8303:
8302:
8301:
8298:
8296:
8293:
8291:
8288:
8286:
8283:
8281:
8278:
8276:
8273:
8272:
8270:
8268:
8264:
8258:
8255:
8251:
8248:
8244:
8241:
8239:
8236:
8235:
8234:
8231:
8230:
8229:
8226:
8222:
8219:
8217:
8214:
8212:
8209:
8207:
8204:
8203:
8202:
8199:
8198:
8196:
8194:
8190:
8187:
8185:
8181:
8175:
8172:
8170:
8167:
8163:
8160:
8159:
8158:
8155:
8153:
8150:
8146:
8145:loss function
8143:
8142:
8141:
8138:
8134:
8131:
8129:
8126:
8124:
8121:
8120:
8119:
8116:
8114:
8111:
8109:
8106:
8102:
8099:
8097:
8094:
8092:
8086:
8083:
8082:
8081:
8078:
8074:
8071:
8069:
8066:
8064:
8061:
8060:
8059:
8056:
8052:
8049:
8047:
8044:
8043:
8042:
8039:
8035:
8032:
8031:
8030:
8027:
8023:
8020:
8019:
8018:
8015:
8013:
8010:
8008:
8005:
8003:
8000:
7999:
7997:
7995:
7991:
7987:
7983:
7978:
7974:
7960:
7957:
7955:
7952:
7950:
7947:
7945:
7942:
7941:
7939:
7937:
7933:
7927:
7924:
7922:
7919:
7917:
7914:
7913:
7911:
7907:
7901:
7898:
7896:
7893:
7891:
7888:
7886:
7883:
7881:
7878:
7876:
7873:
7871:
7868:
7867:
7865:
7863:
7859:
7853:
7850:
7848:
7847:Questionnaire
7845:
7843:
7840:
7836:
7833:
7831:
7828:
7827:
7826:
7823:
7822:
7820:
7818:
7814:
7808:
7805:
7803:
7800:
7798:
7795:
7793:
7790:
7788:
7785:
7783:
7780:
7778:
7775:
7773:
7770:
7769:
7767:
7765:
7761:
7757:
7753:
7748:
7744:
7730:
7727:
7725:
7722:
7720:
7717:
7715:
7712:
7710:
7707:
7705:
7702:
7700:
7697:
7695:
7692:
7690:
7687:
7685:
7682:
7680:
7677:
7675:
7674:Control chart
7672:
7670:
7667:
7665:
7662:
7660:
7657:
7656:
7654:
7652:
7648:
7642:
7639:
7635:
7632:
7630:
7627:
7626:
7625:
7622:
7620:
7617:
7615:
7612:
7611:
7609:
7607:
7603:
7597:
7594:
7592:
7589:
7587:
7584:
7583:
7581:
7577:
7571:
7568:
7567:
7565:
7563:
7559:
7547:
7544:
7542:
7539:
7537:
7534:
7533:
7532:
7529:
7527:
7524:
7523:
7521:
7519:
7515:
7509:
7506:
7504:
7501:
7499:
7496:
7494:
7491:
7489:
7486:
7484:
7481:
7479:
7476:
7475:
7473:
7471:
7467:
7461:
7458:
7456:
7453:
7449:
7446:
7444:
7441:
7439:
7436:
7434:
7431:
7429:
7426:
7424:
7421:
7419:
7416:
7414:
7411:
7409:
7406:
7404:
7401:
7400:
7399:
7396:
7395:
7393:
7391:
7387:
7384:
7382:
7378:
7374:
7370:
7365:
7361:
7355:
7352:
7350:
7347:
7346:
7343:
7339:
7332:
7327:
7325:
7320:
7318:
7313:
7312:
7309:
7302:
7297:
7293:
7292:
7281:
7275:
7271:
7270:
7264:
7260:
7258:9780470512845
7254:
7250:
7246:
7241:
7237:
7231:
7227:
7226:
7221:
7217:
7213:
7207:
7203:
7198:
7183:
7179:
7172:
7167:
7162:
7157:
7153:
7149:
7148:
7143:
7138:
7134:
7128:
7124:
7119:
7115:
7111:
7107:
7103:
7099:
7095:
7088:
7083:
7079:
7073:
7069:
7064:
7060:
7054:
7050:
7049:
7043:
7039:
7035:
7030:
7026:
7020:
7016:
7012:
7007:
7003:
6998:
6994:
6990:
6986:
6982:
6977:
6973:
6969:
6964:
6959:
6955:
6951:
6947:
6943:
6939:
6935:
6931:
6926:
6911:
6907:
6903:
6899:
6895:
6891:
6887:
6880:
6875:
6871:
6867:
6863:
6859:
6855:
6851:
6847:
6843:
6838:
6834:
6830:
6826:
6822:
6818:
6814:
6810:
6806:
6802:
6798:
6794:
6790:
6786:
6782:
6778:
6774:
6770:
6766:
6762:
6758:
6754:
6750:
6746:
6742:
6738:
6731:
6727:
6723:
6719:
6713:
6709:
6704:
6700:
6696:
6692:
6688:
6684:
6680:
6679:
6673:
6669:
6663:
6659:
6655:
6654:
6648:
6644:
6638:
6634:
6630:
6625:
6621:
6616:
6612:
6608:
6603:
6599:
6597:9780470110126
6593:
6589:
6585:
6580:
6579:
6572:
6568:
6564:
6558:
6554:
6553:
6547:
6543:
6537:
6533:
6528:
6524:
6520:
6516:
6515:
6509:
6505:
6499:
6495:
6490:
6486:
6482:
6478:
6474:
6470:
6466:
6465:
6459:
6455:
6451:
6447:
6443:
6439:
6435:
6431:
6427:
6423:
6419:
6414:
6410:
6404:
6400:
6395:
6391:
6384:
6379:
6375:
6369:
6365:
6360:
6356:
6352:
6348:
6342:
6338:
6334:
6329:
6324:
6320:
6315:
6311:
6307:
6303:
6299:
6293:
6289:
6285:
6281:
6277:
6271:
6267:
6262:
6258:
6254:
6250:
6246:
6242:
6238:
6233:
6229:
6225:
6221:
6217:
6213:
6209:
6204:
6200:
6196:
6195:
6187:
6183:
6179:
6178:
6163:
6154:
6145:
6139:
6134:
6128:
6123:
6117:
6113:
6107:
6099:
6095:
6091:
6087:
6082:
6077:
6073:
6069:
6062:
6054:
6050:
6046:
6042:
6035:
6027:
6023:
6019:
6015:
6011:
6007:
6000:
5994:
5989:
5987:
5978:
5974:
5970:
5966:
5962:
5958:
5951:
5944:
5925:
5921:
5914:
5907:
5899:
5895:
5890:
5885:
5880:
5875:
5871:
5867:
5863:
5859:
5858:
5853:
5846:
5838:
5831:
5823:
5817:
5813:
5809:
5804:
5799:
5795:
5787:
5772:
5768:
5762:
5747:
5740:
5733:
5725:
5724:Dice Insights
5721:
5715:
5708:
5703:
5688:
5681:
5678:Jakl, Tomas.
5674:
5666:
5660:
5656:
5652:
5648:
5644:
5640:
5633:
5614:
5610:
5603:
5596:
5585:
5582:Bruns, Pete.
5578:
5570:
5564:
5560:
5556:
5551:
5546:
5542:
5535:
5519:
5515:
5509:
5494:
5487:
5480:
5472:
5468:
5464:
5460:
5453:
5445:
5441:
5437:
5433:
5428:
5423:
5419:
5415:
5408:
5402:
5397:
5389:
5385:
5381:
5377:
5370:
5363:
5358:
5351:
5346:
5331:
5325:
5321:
5314:
5313:
5306:
5298:
5294:
5290:
5286:
5282:
5278:
5274:
5270:
5263:
5254:
5249:
5245:
5241:
5238:(2): 328â42.
5237:
5233:
5229:
5222:
5213:
5207:
5202:
5196:
5191:
5183:
5179:
5175:
5171:
5167:
5163:
5156:
5150:
5145:
5137:
5133:
5129:
5125:
5121:
5117:
5113:
5109:
5105:
5101:
5094:
5086:
5082:
5078:
5074:
5070:
5066:
5062:
5058:
5054:
5050:
5043:
5035:
5031:
5026:
5021:
5017:
5013:
5009:
5005:
5001:
4997:
4993:
4986:
4980:, p. 16.
4979:
4974:
4968:, p. 13.
4967:
4962:
4954:
4950:
4945:
4940:
4936:
4932:
4927:
4922:
4918:
4914:
4910:
4903:
4897:
4892:
4884:
4880:
4876:
4872:
4868:
4864:
4860:
4856:
4849:
4843:
4838:
4832:
4827:
4825:
4818:
4813:
4805:
4801:
4797:
4793:
4789:
4785:
4781:
4774:
4767:(1): 429â434.
4766:
4762:
4755:
4748:(3): 293â318.
4747:
4743:
4736:
4729:
4721:
4717:
4712:
4707:
4703:
4699:
4695:
4688:
4680:
4676:
4671:
4666:
4662:
4658:
4654:
4647:
4639:
4635:
4631:
4627:
4623:
4619:
4612:
4604:
4600:
4595:
4590:
4586:
4582:
4578:
4571:
4561:
4551:
4541:
4531:
4521:
4511:
4492:
4488:
4484:
4480:
4476:
4472:
4468:
4464:
4460:
4453:
4446:
4427:
4423:
4419:
4412:
4405:
4403:
4394:
4390:
4386:
4382:
4378:
4374:
4367:
4359:
4355:
4351:
4347:
4343:
4339:
4335:
4331:
4324:
4316:
4312:
4307:
4302:
4298:
4294:
4290:
4286:
4285:J. Chem. Phys
4282:
4275:
4273:
4265:
4261:
4257:
4250:
4243:
4235:
4231:
4227:
4223:
4219:
4215:
4208:
4206:
4197:
4193:
4189:
4185:
4181:
4177:
4173:
4169:
4162:
4151:
4147:
4143:
4139:
4135:
4131:
4127:
4123:
4119:
4112:
4105:
4096:
4091:
4087:
4083:
4079:
4072:
4063:
4058:
4054:
4050:
4046:
4039:
4031:
4027:
4023:
4017:
4013:
4009:
4005:
4004:
3999:
3992:
3990:
3982:
3978:
3976:9780387202686
3972:
3968:
3967:
3959:
3957:
3948:
3944:
3938:
3930:
3926:
3920:
3912:
3908:
3904:
3900:
3893:
3885:
3881:
3874:
3867:
3859:
3855:
3850:
3845:
3840:
3835:
3831:
3827:
3823:
3819:
3815:
3808:
3800:
3796:
3789:
3781:
3777:
3773:
3769:
3765:
3761:
3757:
3750:
3743:
3738:
3736:
3728:
3727:Eckhardt 1987
3723:
3716:
3711:
3709:
3707:
3698:
3694:
3690:
3686:
3682:
3678:
3671:
3663:
3659:
3655:
3651:
3647:
3643:
3636:
3628:
3624:
3620:
3616:
3612:
3608:
3603:
3598:
3594:
3590:
3583:
3575:
3571:
3567:
3563:
3560:(1): 070001.
3559:
3555:
3548:
3540:
3533:
3525:
3521:
3514:
3512:
3500:
3499:
3491:
3489:
3487:
3485:
3476:
3472:
3468:
3464:
3459:
3454:
3450:
3446:
3439:
3432:
3428:
3424:
3423:
3415:
3413:
3411:
3402:
3398:
3391:
3389:
3380:
3376:
3372:
3368:
3364:
3360:
3353:
3345:
3341:
3337:
3333:
3326:
3318:
3314:
3310:
3306:
3302:
3298:
3294:
3290:
3283:
3275:
3271:
3267:
3263:
3259:
3255:
3251:
3247:
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2209:geometallurgy
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2205:geostatistics
2202:
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2175:probabilistic
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1889:Finite volume
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1490:metaheuristic
1487:
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1451:hydrogen bomb
1448:
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1408:
1401:
1399:
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1369:
1366:
1365:probabilistic
1355:
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1149:
1146:be such that
1145:
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1100:
1089:
1085:
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1077:
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1016:
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369:
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325:
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313:cost overruns
310:
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114:
113:deterministic
110:
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99:
98:
90:
86:
82:
78:
76:
72:
68:
67:deterministic
64:
60:
57:
54:that rely on
53:
50:
49:computational
46:
42:
35:
30:
26:
22:
9619:
9607:
9588:
9581:
9493:Econometrics
9443: /
9426:Chemometrics
9403:Epidemiology
9396: /
9369:Applications
9211:ARIMA model
9158:Q-statistic
9107:Stationarity
9003:Multivariate
8946: /
8942: /
8940:Multivariate
8938: /
8878: /
8874: /
8648:Bayes factor
8547:Signed rank
8459:
8433:
8425:
8413:
8108:Completeness
7944:Cohort study
7842:Opinion poll
7777:Missing data
7764:Study design
7719:Scatter plot
7641:Scatter plot
7634:Spearman's Ï
7596:Grouped data
7268:
7244:
7224:
7201:
7189:. Retrieved
7182:the original
7177:
7151:
7145:
7122:
7097:
7093:
7067:
7047:
7033:
7010:
7001:
6984:
6980:
6937:
6933:
6917:. Retrieved
6910:the original
6889:
6885:
6848:(1): 10â25.
6845:
6841:
6808:
6804:
6756:
6752:
6736:
6707:
6682:
6676:
6656:. New York:
6652:
6628:
6619:
6606:
6577:
6567:the original
6551:
6531:
6513:
6493:
6468:
6462:
6421:
6417:
6398:
6389:
6363:
6318:
6309:
6287:
6284:Binder, Kurt
6265:
6240:
6236:
6214:(1): 73â79.
6211:
6207:
6198:
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6071:
6067:
6061:
6044:
6040:
6034:
6009:
6005:
5999:
5960:
5956:
5943:
5933:December 12,
5931:. Retrieved
5924:the original
5906:
5861:
5855:
5845:
5836:
5830:
5793:
5786:
5774:. Retrieved
5770:
5761:
5749:. Retrieved
5745:
5732:
5723:
5714:
5702:
5690:. Retrieved
5686:
5673:
5638:
5632:
5620:. Retrieved
5613:the original
5608:
5595:
5577:
5540:
5534:
5522:. Retrieved
5518:the original
5508:
5496:. Retrieved
5492:
5479:
5462:
5458:
5452:
5417:
5413:
5407:
5396:
5379:
5375:
5369:
5357:
5345:
5333:. Retrieved
5311:
5305:
5272:
5268:
5262:
5235:
5231:
5221:
5212:
5201:
5190:
5165:
5161:
5155:
5149:Baeurle 2009
5144:
5103:
5099:
5093:
5052:
5048:
5042:
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4995:
4985:
4973:
4961:
4916:
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4848:
4837:
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4764:
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4745:
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4646:
4621:
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4584:
4580:
4570:
4560:
4550:
4540:
4530:
4520:
4510:
4498:. Retrieved
4491:the original
4462:
4458:
4445:
4433:. Retrieved
4426:the original
4421:
4417:
4376:
4372:
4366:
4333:
4329:
4323:
4288:
4284:
4263:
4259:
4255:
4242:
4217:
4214:Phys. Rev. A
4213:
4174:(13): 2159.
4171:
4167:
4161:
4150:the original
4121:
4118:Phys. Rev. E
4117:
4104:
4085:
4081:
4071:
4052:
4048:
4038:
4002:
3980:
3965:
3946:
3937:
3928:
3919:
3902:
3898:
3892:
3883:
3879:
3866:
3821:
3817:
3807:
3798:
3794:
3788:
3766:(3): 42â63.
3763:
3759:
3749:
3722:
3680:
3676:
3670:
3645:
3641:
3635:
3592:
3588:
3582:
3557:
3553:
3547:
3538:
3532:
3523:
3497:
3448:
3444:
3438:
3430:
3421:
3396:
3362:
3358:
3352:
3338:(2): 34â45.
3335:
3331:
3325:
3292:
3288:
3282:
3241:
3237:
3231:
3182:
3178:
3172:
3163:
3153:
3128:
3124:
3118:
3106:
2974:
2964:
2962:
2957:
2945:
2929:
2916:
2897:
2863:
2852:
2832:
2790:well-behaved
2787:
2759:
2691:
2675:
2670:
2649:
2625:
2606:
2602:
2555:
2538:architecture
2527:
2493:
2490:
2473:
2462:
2449:
2441:
2406:
2405:conditions (
2395:normal curve
2390:
2387:type I error
2380:
2367:Path tracing
2365:
2343:
2333:
2322:analysis of
2313:
2177:analysis in
2168:
2147:astrophysics
2095:heat shields
2080:
1936:
1817:Multiphysics
1768:
1765:Applications
1747:
1743:
1734:brown dwarfs
1723:
1712:
1702:
1679:
1671:
1663:pseudorandom
1651:
1639:
1635:
1629:
1625:
1613:
1607:
1590:
1584:
1580:
1578:
1569:
1565:
1546:in advanced
1541:
1510:
1475:
1418:
1412:
1403:
1391:
1387:Enrico Fermi
1376:
1361:
1344:
1334:
1330:
1326:
1322:
1321:)ln(2/0.01)/
1318:
1314:
1310:
1309:= 99%, then
1306:
1304:
1191:
1186:
1182:
1178:
1174:
1170:
1166:
1162:
1158:
1151:
1147:
1140:
1133:
1126:
1119:
1115:
1111:
1107:
1103:
1101:
1098:
1087:
1083:
1079:
1072:
1068:
1064:
1055:
1051:
1044:
1040:
1036:
1029:
1025:
1018:
1014:
1010:
1006:
1002:
998:
994:
987:
983:
976:
972:
968:
966:
908:
903:
902:
897:
890:
888:
882:
875:
871:
868:
859:
855:
851:
837:
829:
825:
811:
800:
793:
786:
777:
773:
767:
764:
760:
754:
747:
737:
730:
723:
716:
709:
707:
702:
698:
694:
692:
685:
680:
676:
672:
664:
660:
656:
654:
644:
636:
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624:
620:
618:
612:
608:
604:
601:
592:
588:
584:
574:
567:
563:
560:
556:
553:
549:
542:
540:
529:
525:
521:
516:
509:
505:
501:
492:
488:
484:
481:
477:
474:
470:
463:
461:
456:
452:
448:
444:
440:
436:
432:
428:
423:
419:
415:
407:
402:
387:
383:
360:
344:Markov chain
317:
290:
264:
252:optimization
248:mathematical
241:
229:
218:
210:
132:
96:
87:
83:
79:
44:
40:
39:
25:
9621:WikiProject
9536:Cartography
9498:Jurimetrics
9450:Reliability
9181:Time domain
9160:(LjungâBox)
9082:Time-series
8960:Categorical
8944:Time-series
8936:Categorical
8871:(Bernoulli)
8706:Correlation
8686:Correlation
8482:JarqueâBera
8454:Chi-squared
8216:M-estimator
8169:Asymptotics
8113:Sufficiency
7880:Interaction
7792:Replication
7772:Effect size
7729:Violin plot
7709:Radar chart
7689:Forest plot
7679:Correlogram
7629:Kendall's Ï
6919:November 1,
6759:(6): 1087.
6521:. pp.
5751:October 28,
5692:October 28,
5622:October 28,
5498:October 28,
5206:Golden 1979
4817:Ripley 1987
4379:(1): 1â25.
4088:: 171â208.
3648:: 451â459.
3541:. Springer.
3164:OR/MS Today
2700:Integration
2534:video games
2519:Computer Go
2469:search tree
2165:Engineering
2099:aerodynamic
2010:von Neumann
1944:Integration
1771:uncertainty
1667:simulations
1621:simulation.
1617:simulation.
1591:Monte Carlo
1581:Monte Carlo
1575:Definitions
1542:The use of
1494:Alan Turing
1431:simulations
1419:Monte Carlo
1381:, in which
1161:for finite
1114:Let 0 <
1039:; for i =
757:simulations
422:by running
293:uncertainty
238:Application
139:unit square
9637:Categories
9488:Demography
9206:ARMA model
9011:Regression
8588:(Friedman)
8549:(Wilcoxon)
8487:Normality
8477:Lilliefors
8424:Student's
8300:Resampling
8174:Robustness
8162:divergence
8152:Efficiency
8090:(monotone)
8085:Likelihood
8002:Population
7835:Stratified
7787:Population
7606:Dependence
7562:Count data
7493:Percentile
7470:Dispersion
7403:Arithmetic
7338:Statistics
6934:Biophys. J
6586:. p.
5746:Ifremer.fr
5687:Arimaa.com
5275:: 110002.
4926:1707.02212
3949:: 143â182.
3683:: 93â103.
3602:2105.09512
3238:Biometrika
3093:References
3026:Ergodicity
2977:Elishakoff
2971:Philosophy
2884:samplers.
2779:dimensions
2628:harassment
2581:See also:
2517:See also:
2504:Battleship
2403:asymptotic
2216:flowsheets
2075:See also:
1994:Scientists
1843:Potentials
1832:Simulation
1603:simulation
1599:Sawilowsky
1556:resampling
1447:Los Alamos
1189:such that
993:is within
537:An example
412:population
384:mean field
111:Perform a
63:randomness
52:algorithms
8869:Logistic
8636:posterior
8562:Rank sum
8310:Jackknife
8305:Bootstrap
8123:Bootstrap
8058:Parameter
8007:Statistic
7802:Statistic
7714:Run chart
7699:Pie chart
7694:Histogram
7684:Fan chart
7659:Bar chart
7541:L-moments
7428:Geometric
7191:March 15,
6699:189849365
6633:Wiley-VCH
6323:CiteSeerX
6257:117867762
6201:: 96â108.
5977:240435973
5798:CiteSeerX
5589:(Report).
5545:CiteSeerX
5422:CiteSeerX
5297:228828681
4978:Vose 2008
4966:Vose 2008
4953:118895524
4919:(1): 66.
4883:114260173
4720:117725141
4679:119809371
4589:CiteSeerX
4350:0956-375X
3427:CRC Press
3365:: 56â67.
3317:123468109
3309:0162-1459
3266:0006-3444
3207:0021-9606
3098:Citations
2344:ab initio
2143:detectors
2035:Richtmyer
1807:Mechanics
1561:LAAS-CNRS
1285:ϵ
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