22:
620:
461:
347:
260:
716:
468:
168:
354:
644:
96:
267:
734:
176:
652:
615:{\displaystyle W={\frac {1}{J}}\sum _{j=1}^{J}\left({\frac {1}{L-1}}\sum _{i=1}^{L}(x_{i}^{(j)}-{\overline {x}}_{j})^{2}\right)}
99:
43:
105:
737:
compares whether the mean of the first x percent of a chain and the mean of the last y percent of a chain match.
98:
Monte Carlo simulations (chains) are started with different initial values. The samples from the respective
892:
778:
Gelman, Andrew; Rubin, Donald B. (1992). "Inference from
Iterative Simulation Using Multiple Sequences".
170:(of the j-th simulation), the variance between the chains and the variance in the chains is estimated:
887:
829:
68:
456:{\displaystyle B={\frac {L}{J-1}}\sum _{j=1}^{J}({\overline {x}}_{j}-{\overline {x}}_{*})^{2}}
787:
8:
791:
854:
803:
756:
629:
81:
845:
Vats, Dootika; Knudson, Christina (2021). "Revisiting the Gelman–Rubin
Diagnostic".
747:
Vats, Dootika; Knudson, Christina (2021). "Revisiting the Gelman–Rubin
Diagnostic".
342:{\displaystyle {\overline {x}}_{*}={\frac {1}{J}}\sum _{j=1}^{J}{\overline {x}}_{j}}
864:
795:
766:
881:
799:
255:{\displaystyle {\overline {x}}_{j}={\frac {1}{L}}\sum _{i=1}^{L}x_{i}^{(j)}}
807:
868:
770:
859:
761:
41:
parameter to this template to explain the issue with the article.
831:
7.4 Monitoring
Convergence | Advanced Statistical Computing
711:{\displaystyle R={\frac {{\frac {L-1}{L}}W+{\frac {1}{L}}B}{W}}}
622:
Averaged variances of the individual chains across all chains
722:
When L tends to infinity and B tends to zero, R tends to 1.
655:
632:
471:
357:
270:
179:
108:
84:
725:
A different formula is given by Vats & Knudson.
710:
638:
614:
455:
341:
254:
162:
90:
879:
163:{\displaystyle x_{1}^{(j)},\dots ,x_{L}^{(j)}}
31:needs attention from an expert in Mathematics
67:allows a statement about the convergence of
844:
777:
746:
626:An estimate of the Gelman-Rubin statistic
858:
760:
880:
46:may be able to help recruit an expert.
15:
463:Variance of the means of the chains
13:
14:
904:
827:
102:are discarded. From the samples
20:
728:
349:Mean of the means of all chains
838:
821:
598:
572:
566:
553:
444:
403:
247:
241:
155:
149:
125:
119:
1:
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740:
74:
586:
432:
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7:
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909:
834:– via bookdown.org.
69:Monte Carlo simulations
44:WikiProject Mathematics
712:
640:
616:
552:
508:
457:
402:
343:
321:
256:
230:
164:
92:
65:Gelman-Rubin statistic
800:10.1214/ss/1177011136
713:
641:
617:
532:
488:
458:
382:
344:
301:
262:Mean value of chain j
257:
210:
165:
93:
653:
630:
469:
355:
268:
177:
106:
82:
893:Monte Carlo methods
847:Statistical Science
792:1992StaSc...7..457G
780:Statistical Science
749:Statistical Science
576:
251:
159:
129:
708:
636:
612:
556:
453:
339:
252:
231:
160:
139:
109:
88:
888:Estimation theory
869:10.1214/20-STS812
771:10.1214/20-STS812
735:Geweke Diagnostic
706:
697:
681:
646:then results as
639:{\displaystyle R}
589:
530:
486:
435:
415:
380:
331:
299:
280:
208:
189:
91:{\displaystyle J}
61:
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33:. Please add a
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828:Peng, Roger D.
826:
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650:
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786:(4): 457–472.
775:
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100:burn-in phases
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569:
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29:This article
27:
18:
17:
850:
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732:
729:Alternatives
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64:
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52:January 2024
49:
38:
34:
30:
882:Categories
860:1812.09384
816:References
762:1812.09384
741:Literature
75:Definition
672:−
587:¯
578:−
534:∑
524:−
490:∑
439:∗
433:¯
424:−
413:¯
384:∑
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329:¯
303:∑
284:∗
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212:∑
187:¯
134:…
808:2246093
788:Bibcode
806:
35:reason
855:arXiv
853:(4).
804:JSTOR
757:arXiv
755:(4).
37:or a
733:The
63:The
39:talk
865:doi
796:doi
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