Kolmogorov–Smirnov, Fluctuation, and Z_g Tests for Convergence of Markov Chain Monte Carlo Draws

References

• Billingsley , P. ( 1968 ). Convergence of Probability Measures. , 1st ed. . New York : Wiley .
   Google Scholar
• Cowles , M. K. , Carlin , B. P. ( 1996 ). Markov chain Monte Carlo convergence diagnostics: a comparative review . J. Amer. Statist. Assoc. 91 : 883 – 904 .
   Web of Science ®Google Scholar
• Donsker , M. ( 1952 ). Justification and extension of Doob's heuristic approach to the Kolmogorov–Smirnov theorems . Ann. Mathemat. Statist. 23 : 277 – 281 .
   Google Scholar
• Doob , J. L. ( 1949 ). Heuristic approach to the Kolmogorov–Smirnov theorems . Ann. Mathemat. Statist. 20 : 393 – 403 .
   Google Scholar
• Feller , W. ( 1948 ). On the Kolmogorov–Smirnov limit theorems for empirical distributions . Ann. Mathemat. Statist. 19 : 177 – 189 .
   Google Scholar
• Gelman , A. , Carlin , J. , Stern , H. , Rubin , D. ( 2004 ). Bayesian Data Analysis. , 2nd ed. New York : Chapman and Hall .
   Google Scholar
• Geweke , J. ( 1992 ). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments . In: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. , Smith , A. F. M. , eds. Bayesian Statistics 4 . New York : Oxford University Press .
   Google Scholar
• Goldman , E. , Radchenko , S. , Nakatsuma , T. , Tsurumi , H. ( 2001 ). A Bayesian test of stationarity in a regression model with an ARMA error term . Proc. Annual Meet. Amer. Statist. Assoc. August 5–9 .
   Google Scholar
• Heidelberger , P. , Welch , P. D. ( 1983 ). Simulation run length control in the presence of an initial transient . Operat. Res. 31 : 1109 – 1144 .
   Web of Science ®Google Scholar
• Kolmogorov , A. ( 1933 ). Sulla determinazione empirica di une legge di distribuzione . Inst. Ital. Attwari 4 : 83 – 91 .
   Google Scholar
• Ploberger , W. , Krämer , W. , Kontrus , K. ( 1989 ). A new test for structural stability in the linear regression model . J. Econometrics 40 : 307 – 318 .
   Web of Science ®Google Scholar
• Raftery , A. E. , Lewis , S. M. ( 1996 ). Implementing MCMC . In: Gilks , W. R. , Spiegelhalter , D. , Richardson , S. , eds. Markov Chain Monte Carlo in Practice . London : Chapman and Hall , pp. 115 – 130 .
   Google Scholar
• Robert , C. P. , Casella , G. ( 2004 ). Monte Carlo Statistical Methods. , 2nd ed. New York : Springer .
   Google Scholar
• Smirnov , N. ( 1939a ). On the estimation of the discrepancy between empirical curves of distribution for two independent samples . Bull. Mathématique de l'Université de Moscou 2 : fsc.2 .
   Google Scholar
• Smirnov , N. ( 1939b ). Sur lesécarts de la courbe de distribution empirique . Res. Math. (Mat. Sbornik) (NS) 6 : 3 – 26 .
   Google Scholar
• Tsurumi , H. , Shimizu , H. ( 2008 ). Bayesian inference of the regression model with error terms following the exponential power distribution and unbiasedness of the LAD estimator . Commun. Statist. 37 : 2 .
   Google Scholar