102:
49:
1503:(MAE) instead of the root mean square deviation. MAE possesses advantages in interpretability over RMSD. MAE is the average of the absolute values of the errors. MAE is fundamentally easier to understand than the square root of the average of squared errors. Furthermore, each error influences MAE in direct proportion to the absolute value of the error, which is not the case for RMSD.
1649:, normalized root mean square deviation (NRMSD), coefficient of variation (CV), and percent RMS are used to quantify the uniformity of flow behavior such as velocity profile, temperature distribution, or gas species concentration. The value is compared to industry standards to optimize the design of flow and thermal equipment and processes.
406:
202:
RMSD is always non-negative, and a value of 0 (almost never achieved in practice) would indicate a perfect fit to the data. In general, a lower RMSD is better than a higher one. However, comparisons across different types of data would be invalid because the measure is dependent on the scale of the
975:
Normalizing the RMSD facilitates the comparison between datasets or models with different scales. Though there is no consistent means of normalization in the literature, common choices are the mean or the range (defined as the maximum value minus the minimum value) of the measured data:
195:(or prediction errors) when computed out-of-sample (aka on the full set, referencing a true value rather than an estimate). The RMSD serves to aggregate the magnitudes of the errors in predictions for various data points into a single measure of predictive power. RMSD is a measure of
763:
206:
RMSD is the square root of the average of squared errors. The effect of each error on RMSD is proportional to the size of the squared error; thus larger errors have a disproportionately large effect on RMSD. Consequently, RMSD is sensitive to
965:
569:
286:
1057:
791:
In some disciplines, the RMSD is used to compare differences between two things that may vary, neither of which is accepted as the "standard". For example, when measuring the average difference between two time series
1489:
1122:
1224:
1979:
1699:
1390:
1333:
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2020:
609:
665:
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823:
401:{\displaystyle \operatorname {RMSD} ({\hat {\theta }})={\sqrt {\operatorname {MSE} ({\hat {\theta }})}}={\sqrt {\operatorname {E} (({\hat {\theta }}-\theta )^{2})}}.}
274:
649:
480:
472:
161:) is either one of two closely related and frequently used measures of the differences between true or predicted values on the one hand and observed values or an
2350:
191:
when the calculations are performed over the data sample that was used for estimation (and are therefore always in reference to an estimate) and are called
1768:
132:
2013:
1980:
ANSI/BPI-2400-S-2012: Standard
Practice for Standardized Qualification of Whole-House Energy Savings Predictions by Calibration to Energy Use History
982:
1144:. In many cases, especially for smaller samples, the sample range is likely to be affected by the size of sample which would hamper comparisons.
1611:
1532:
31:
1417:
2415:
1817:
Willmott, Cort; Matsuura, Kenji (2006). "On the use of dimensioned measures of error to evaluate the performance of spatial interpolators".
2006:
2149:
1062:
1157:
17:
1635:, RMSD (and RMSZ) is used to measure the deviation of the molecular internal coordinates deviate from the restraints library values.
2056:
1881:
2164:
1575:, the RMSD is used to assess how well mathematical or computational models of behavior explain the empirically observed behavior.
199:, to compare forecasting errors of different models for a particular dataset and not between datasets, as it is scale-dependent.
125:
1151:(IQR). When dividing the RMSD with the IQR the normalized value gets less sensitive for extreme values in the target variable.
1136:(NRMSD or NRMSE), and often expressed as a percentage, where lower values indicate less residual variance. This is also called
73:
68:
2410:
1689:
187:
118:
1903:
2154:
1624:
In the simulation of energy consumption of buildings, the RMSE and CV(RMSE) are used to calibrate models to measured
1338:
1284:
2376:
2237:
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1600:, a measure used to assess how well a method to reconstruct an image performs relative to the original image.
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88:
78:
2106:
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1604:
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1147:
Another possible method to make the RMSD a more useful comparison measure is to divide the RMSD by the
83:
1769:"Components of information for multiple resolution comparison between maps that share a real variable"
230:
2096:
2091:
1229:
758:{\displaystyle \operatorname {RMSD} ={\sqrt {\frac {\sum _{t=1}^{T}(y_{t}-{\hat {y}}_{t})^{2}}{T}}}.}
1733:
578:
2192:
1923:
1694:
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1404:
1137:
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2187:
2182:
1572:
960:{\displaystyle \operatorname {RMSD} ={\sqrt {\frac {\sum _{t=1}^{T}(x_{1,t}-x_{2,t})^{2}}{T}}}.}
2124:
1918:
1728:
1679:
196:
1968:
564:{\displaystyle \operatorname {RMSD} ={\sqrt {{\frac {1}{n}}\sum _{i=1}^{n}(X_{i}-x_{0})^{2}}}}
1674:
1632:
1614:, the RMSD is used as a measure to estimate the quality of the obtained bundle of structures.
1582:, the RMSD is one measure used to assess the accuracy of spatial analysis and remote sensing.
828:
795:
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63:
58:
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Hyndman, Rob J.; Koehler, Anne B. (2006). "Another look at measures of forecast accuracy".
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450:
1638:
In control theory, the RMSE is used as a quality measure to evaluate the performance of a
8:
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2038:
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93:
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1549:, the RMSD is a measure of the difference between a crystal conformation of the ligand
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659:
different predictions as the square root of the mean of the squares of the deviations:
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1738:
1659:
1568:. Some experts have argued that RMSD is less reliable than Relative Absolute Error.
1904:"Error Measures For Generalizing About Forecasting Methods: Empirical Comparisons"
2322:
2265:
2144:
1593:
1860:
1646:
1639:
1528:
1052:{\displaystyle \mathrm {NRMSD} ={\frac {\mathrm {RMSD} }{y_{\max }-y_{\min }}}}
178:
1838:
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2404:
2207:
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were judged using the RMSD from the test dataset's undisclosed "true" values.
1618:
1589:, RMSD and NRMSD are used to evaluate the calibration of a groundwater model.
1586:
1517:
1513:
181:
of the differences between the observed values and predicted ones. These
1956:
Applied
Groundwater Modeling: Simulation of Flow and Advective Transport
1484:{\displaystyle \mathrm {CV(RMSD)} ={\frac {\mathrm {RMSD} }{\bar {y}}}.}
2301:
2212:
2197:
1521:
40:
2119:
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162:
1607:, the RMSD is used to assess how well a system learns a given model.
1117:{\displaystyle \mathrm {NRMSD} ={\frac {\mathrm {RMSD} }{\bar {y}}}}
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2227:
2114:
1399:
When normalizing by the mean value of the measurements, the term
1219:{\displaystyle \mathrm {RMSDIQR} ={\frac {\mathrm {RMSD} }{IQR}}}
208:
1564:, the RMSD is used to determine whether an economic model fits
1535:
is the measure of the average distance between the atoms of
2306:
2278:
2273:
2250:
1767:
Pontius, Robert; Thontteh, Olufunmilayo; Chen, Hao (2008).
1861:"Coastal Inlets Research Program (CIRP) Wiki - Statistics"
1819:
International
Journal of Geographical Information Science
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may be used to avoid ambiguity. This is analogous to the
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1499:Some researchers have recommended the use of the
447:is a sample of a population with true mean value
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1991:https://kalman-filter.com/root-mean-square-error
1901:
1816:
1041:
1028:
1612:protein nuclear magnetic resonance spectroscopy
1718:
1533:root mean square deviation of atomic positions
1401:coefficient of variation of the RMSD, CV(RMSD)
1385:{\displaystyle Q_{3}={\text{CDF}}^{-1}(0.75),}
32:Root mean square deviation of atomic positions
2014:
1328:{\displaystyle Q_{1}={\text{CDF}}^{-1}(0.25)}
126:
1882:"FAQ: What is the coefficient of variation?"
1902:Armstrong, J. Scott; Collopy, Fred (1992).
2021:
2007:
1128:This value is commonly referred to as the
133:
119:
47:
1922:
1732:
1954:Anderson, M.P.; Woessner, W.W. (1992).
256:with respect to an estimated parameter
14:
2403:
1494:
1407:with the RMSD taking the place of the
2002:
1130:normalized root mean square deviation
415:, the RMSD is the square root of the
276:is defined as the square root of the
2416:Statistical deviation and dispersion
1911:International Journal of Forecasting
1762:
1760:
1721:International Journal of Forecasting
30:For the bioinformatics concept, see
1776:Environmental Ecological Statistics
1700:Normalized estimation error squared
1520:model predicts the behavior of the
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24:
1690:Errors and residuals in statistics
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25:
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474:, then the RMSD of the sample is
1743:10.1016/j.ijforecast.2006.03.001
970:
249:{\displaystyle {\hat {\theta }}}
100:
2377:Pearson correlation coefficient
1984:
1958:(2nd ed.). Academic Press.
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1271:{\displaystyle IQR=Q_{3}-Q_{1}}
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2316:Deep Learning Related Metrics
1969:Ensemble Neural Network Model
1705:
651:with variables observed over
575:The RMSD of predicted values
2411:Point estimation performance
1933:10.1016/0169-2070(92)90008-w
219:
7:
2160:Sensitivity and specificity
1653:
1547:structure based drug design
1516:, to see how effectively a
214:
10:
2432:
1670:Average absolute deviation
1605:computational neuroscience
1598:peak signal-to-noise ratio
1596:, the RMSD is part of the
426:
147:root mean square deviation
29:
18:Root-mean-square deviation
2385:
2359:
2336:
2315:
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2236:
2173:
2105:
2037:
1839:10.1080/13658810500286976
1796:10.1007/s10651-007-0043-y
1695:Coefficient of Variation
1405:coefficient of variation
1138:Coefficient of Variation
2188:Calinski-Harabasz index
1573:experimental psychology
851:{\displaystyle x_{2,t}}
818:{\displaystyle x_{1,t}}
655:times, is computed for
269:{\displaystyle \theta }
1680:Mean squared deviation
1485:
1386:
1329:
1272:
1220:
1118:
1053:
961:
898:
858:, the formula becomes
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819:
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645:
644:{\displaystyle y_{t},}
605:
565:
522:
468:
402:
270:
250:
155:root mean square error
107:Mathematics portal
2351:Intra-list Similarity
1675:Mean signed deviation
1633:X-ray crystallography
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467:{\displaystyle x_{0}}
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1626:building performance
1617:Submissions for the
1418:
1339:
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770:cross-sectional data
768:(For regressions on
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1831:2006IJGIS..20...89W
1788:2008EnvES..15..111P
1665:Mean absolute error
1566:economic indicators
1501:mean absolute error
1495:Mean absolute error
1149:interquartile range
27:Statistical measure
2372:Euclidean distance
2338:Recommender system
2218:Similarity measure
2032:evaluation metrics
1685:Squared deviations
1481:
1409:standard deviation
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1049:
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421:standard deviation
413:unbiased estimator
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278:mean squared error
266:
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2367:Cosine similarity
2203:Hopkins statistic
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1394:quantile function
1392:where CDF is the
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16:(Redirected from
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2390:Confusion matrix
2165:Logarithmic Loss
2030:Machine learning
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1660:Root mean square
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1924:10.1.1.423.508
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1809:
1782:(2): 111–142.
1756:
1727:(4): 679–688.
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1094:
1091:
1085:
1081:
1078:
1075:
1072:
1069:
1043:
1039:
1035:
1030:
1026:
1020:
1017:
1014:
1011:
1005:
1001:
998:
995:
992:
989:
972:
969:
968:
967:
956:
950:
944:
940:
934:
931:
928:
924:
920:
915:
912:
909:
905:
901:
896:
891:
888:
885:
881:
873:
870:
845:
842:
839:
835:
812:
809:
806:
802:
766:
765:
754:
748:
742:
738:
732:
725:
722:
715:
710:
706:
702:
697:
692:
689:
686:
682:
674:
671:
640:
635:
631:
598:
591:
588:
573:
572:
556:
552:
546:
542:
538:
533:
529:
525:
520:
515:
512:
509:
505:
499:
496:
489:
486:
461:
457:
442:
436:
428:
425:
409:
408:
397:
392:
387:
383:
379:
376:
370:
367:
361:
358:
355:
352:
347:
342:
336:
333:
327:
324:
321:
316:
313:
307:
304:
298:
295:
292:
265:
242:
239:
221:
218:
216:
213:
203:numbers used.
179:quadratic mean
173:The RMSD of a
170:
167:
165:on the other.
141:
140:
138:
137:
130:
123:
115:
112:
111:
110:
109:
96:
91:
86:
81:
76:
71:
66:
61:
53:
52:
44:
43:
26:
9:
6:
4:
3:
2:
2428:
2417:
2414:
2412:
2409:
2408:
2406:
2391:
2388:
2387:
2384:
2378:
2375:
2373:
2370:
2368:
2365:
2364:
2362:
2358:
2352:
2349:
2347:
2344:
2343:
2341:
2339:
2335:
2329:
2326:
2324:
2321:
2320:
2318:
2314:
2308:
2305:
2303:
2300:
2299:
2297:
2295:
2291:
2285:
2282:
2280:
2277:
2275:
2272:
2271:
2269:
2267:
2263:
2257:
2254:
2252:
2249:
2247:
2244:
2243:
2241:
2239:
2235:
2229:
2226:
2224:
2221:
2219:
2216:
2214:
2211:
2209:
2208:Jaccard index
2206:
2204:
2201:
2199:
2196:
2194:
2191:
2189:
2186:
2184:
2181:
2180:
2178:
2176:
2172:
2166:
2163:
2161:
2158:
2156:
2153:
2151:
2148:
2146:
2143:
2141:
2138:
2136:
2133:
2131:
2128:
2126:
2123:
2121:
2118:
2116:
2113:
2112:
2110:
2108:
2104:
2098:
2095:
2093:
2090:
2088:
2085:
2083:
2080:
2078:
2075:
2073:
2070:
2068:
2065:
2063:
2060:
2058:
2055:
2053:
2050:
2048:
2045:
2044:
2042:
2040:
2036:
2031:
2024:
2019:
2017:
2012:
2010:
2005:
2004:
2001:
1992:
1987:
1981:
1976:
1970:
1965:
1957:
1950:
1942:
1938:
1934:
1930:
1925:
1920:
1916:
1912:
1905:
1898:
1883:
1877:
1862:
1856:
1848:
1844:
1840:
1836:
1832:
1828:
1825:(1): 89–102.
1824:
1820:
1813:
1805:
1801:
1797:
1793:
1789:
1785:
1781:
1777:
1770:
1763:
1761:
1752:
1748:
1744:
1740:
1735:
1730:
1726:
1722:
1715:
1711:
1701:
1698:
1696:
1693:
1691:
1688:
1686:
1683:
1681:
1678:
1676:
1673:
1671:
1668:
1666:
1663:
1661:
1658:
1657:
1648:
1644:
1641:
1637:
1634:
1630:
1627:
1623:
1620:
1619:Netflix Prize
1616:
1613:
1609:
1606:
1602:
1599:
1595:
1591:
1588:
1584:
1581:
1577:
1574:
1570:
1567:
1563:
1559:
1556:
1552:
1548:
1544:
1541:
1538:
1534:
1530:
1526:
1523:
1519:
1515:
1511:
1510:
1504:
1502:
1478:
1468:
1447:
1414:
1413:
1412:
1410:
1406:
1402:
1397:
1395:
1379:
1373:
1365:
1362:
1352:
1347:
1343:
1319:
1311:
1308:
1298:
1293:
1289:
1263:
1259:
1255:
1250:
1246:
1242:
1239:
1236:
1233:
1210:
1207:
1204:
1184:
1154:
1153:
1152:
1150:
1145:
1143:
1139:
1135:
1131:
1104:
1083:
1037:
1033:
1024:
1003:
979:
978:
977:
971:Normalization
954:
948:
942:
932:
929:
926:
922:
918:
913:
910:
907:
903:
894:
889:
886:
883:
879:
871:
868:
861:
860:
859:
843:
840:
837:
833:
810:
807:
804:
800:
789:
787:
783:
779:
775:
771:
752:
746:
740:
730:
720:
713:
708:
704:
695:
690:
687:
684:
680:
672:
669:
662:
661:
660:
658:
654:
638:
633:
629:
621:
618:
614:
596:
586:
554:
544:
540:
536:
531:
527:
518:
513:
510:
507:
503:
497:
494:
487:
484:
477:
476:
475:
459:
455:
445:
435:
424:
422:
418:
414:
395:
385:
377:
374:
365:
353:
345:
331:
322:
319:
314:
302:
293:
290:
283:
282:
281:
279:
263:
237:
227:
212:
210:
204:
200:
198:
194:
190:
189:
184:
180:
176:
166:
164:
160:
156:
152:
148:
136:
131:
129:
124:
122:
117:
116:
114:
113:
108:
103:
97:
95:
92:
90:
87:
85:
82:
80:
77:
75:
72:
70:
67:
65:
64:Statisticians
62:
60:
57:
56:
55:
54:
50:
46:
45:
42:
39:
38:
33:
19:
1986:
1975:
1964:
1955:
1949:
1917:(1): 69–80.
1914:
1910:
1897:
1885:. Retrieved
1876:
1864:. Retrieved
1855:
1822:
1818:
1812:
1779:
1775:
1724:
1720:
1714:
1587:hydrogeology
1551:conformation
1537:superimposed
1518:mathematical
1507:Applications
1498:
1400:
1398:
1280:
1146:
1141:
1133:
1129:
1127:
974:
790:
785:
781:
777:
773:
767:
656:
652:
617:regression's
612:
574:
440:
433:
430:
410:
223:
205:
201:
192:
186:
172:
158:
154:
150:
146:
144:
1887:19 February
1557:prediction.
1514:meteorology
1142:Percent RMS
185:are called
2405:Categories
2360:Similarity
2302:Perplexity
2213:Rand index
2198:Dunn index
2183:Silhouette
2175:Clustering
2039:Regression
1866:4 February
1706:References
1522:atmosphere
611:for times
183:deviations
41:Statistics
2130:Precision
2082:RMSE/RMSD
1919:CiteSeerX
1729:CiteSeerX
1562:economics
1472:¯
1363:−
1309:−
1256:−
1108:¯
1034:−
919:−
880:∑
724:^
714:−
681:∑
590:^
537:−
504:∑
378:θ
375:−
369:^
366:θ
354:
335:^
332:θ
323:
306:^
303:θ
294:
264:θ
241:^
238:θ
226:estimator
220:Estimator
188:residuals
163:estimator
2346:Coverage
2125:Accuracy
1941:11034360
1847:15407960
1804:21427573
1751:15947215
1654:See also
1540:proteins
417:variance
215:Formulas
209:outliers
197:accuracy
94:Category
89:Articles
79:Journals
74:Notation
69:Glossary
2238:Ranking
2228:SimHash
2115:F-score
1827:Bibcode
1784:Bibcode
1555:docking
439:, ...,
427:Samples
411:For an
177:is the
59:Outline
2135:Recall
1939:
1921:
1845:
1802:
1749:
1731:
1553:and a
1531:, the
1226:where
193:errors
175:sample
2140:Kappa
2057:sMAPE
1937:S2CID
1907:(PDF)
1843:S2CID
1800:S2CID
1772:(PDF)
1747:S2CID
1281:with
1134:error
615:of a
153:) or
2307:BLEU
2279:SSIM
2274:PSNR
2251:NDCG
2072:MSPE
2067:MASE
2062:MAPE
1889:2019
1868:2015
1374:0.75
1335:and
1320:0.25
869:RMSD
825:and
780:and
670:RMSD
485:RMSD
291:RMSD
159:RMSE
151:RMSD
145:The
2328:FID
2294:NLP
2284:IoU
2246:MRR
2223:SMC
2155:ROC
2150:AUC
2145:MCC
2097:MAD
2092:MDA
2077:RMS
2052:MAE
2047:MSE
1929:doi
1835:doi
1792:doi
1739:doi
1645:In
1631:In
1610:In
1603:In
1592:In
1585:In
1580:GIS
1578:In
1571:In
1560:In
1545:In
1527:In
1512:In
1358:CDF
1304:CDF
1140:or
1132:or
1059:or
1042:min
1029:max
788:.)
431:If
320:MSE
2407::
2256:AP
2120:P4
1935:.
1927:.
1913:.
1909:.
1841:.
1833:.
1823:20
1821:.
1798:.
1790:.
1780:15
1778:.
1774:.
1759:^
1745:.
1737:.
1725:22
1723:.
1411:.
1396:.
423:.
280::
211:.
2087:R
2022:e
2015:t
2008:v
1943:.
1931::
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1891:.
1870:.
1849:.
1837::
1829::
1806:.
1794::
1786::
1753:.
1741::
1642:.
1628:.
1542:.
1524:.
1479:.
1469:y
1463:D
1460:S
1457:M
1454:R
1448:=
1444:)
1441:D
1438:S
1435:M
1432:R
1429:(
1426:V
1423:C
1380:,
1377:)
1371:(
1366:1
1353:=
1348:3
1344:Q
1323:)
1317:(
1312:1
1299:=
1294:1
1290:Q
1264:1
1260:Q
1251:3
1247:Q
1243:=
1240:R
1237:Q
1234:I
1211:R
1208:Q
1205:I
1200:D
1197:S
1194:M
1191:R
1185:=
1181:R
1178:Q
1175:I
1172:D
1169:S
1166:M
1163:R
1124:.
1105:y
1099:D
1096:S
1093:M
1090:R
1084:=
1080:D
1077:S
1074:M
1071:R
1068:N
1038:y
1025:y
1019:D
1016:S
1013:M
1010:R
1004:=
1000:D
997:S
994:M
991:R
988:N
955:.
949:T
943:2
939:)
933:t
930:,
927:2
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914:t
911:,
908:1
904:x
900:(
895:T
890:1
887:=
884:t
872:=
844:t
841:,
838:2
834:x
811:t
808:,
805:1
801:x
786:n
782:T
778:i
774:t
753:.
747:T
741:2
737:)
731:t
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709:t
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696:T
691:1
688:=
685:t
673:=
657:T
653:T
639:,
634:t
630:y
613:t
597:t
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571:.
555:2
551:)
545:0
541:x
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524:(
519:n
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511:=
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488:=
460:0
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437:1
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396:.
391:)
386:2
382:)
360:(
357:(
351:E
346:=
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326:(
315:=
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297:(
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120:v
34:.
20:)
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