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Original Articles

MCMC diagnostics for higher dimensions using Kullback Leibler divergence

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Pages 2622-2638 | Received 15 Jun 2016, Accepted 23 May 2017, Published online: 05 Jun 2017

References

  • Rosenthal JS. Minorization conditions and convergence rates for Markov chain Monte Carlo. J Amer Statist Assoc. 1995;90(430):558–566. doi: 10.1080/01621459.1995.10476548
  • Jones GL, Hobert JP. Honest exploration of intractable probability distributions via Markov chain Monte Carlo. Statist Sci. 2001;16(4):312–334. doi: 10.1214/ss/1015346317
  • Roy V, Hobert JP. Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression. J R Stat Soc Ser B Stat Methodol. 2007;69(4):607–623. doi: 10.1111/j.1467-9868.2007.00602.x
  • Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Statist Sci. 1992;7:457–472. doi: 10.1214/ss/1177011136
  • Brooks SP, Gelman A. General methods for monitoring convergence of iterative simulations. J Comput Graph Statist. 1998;7:434–455.
  • Raftery AE, Lewis SM. How many iterations in the Gibbs sampler. In: Bernardo JM, Smith AFM, Dawid AP, Berger JO, editors. Bayesian statistics 4. Oxford: Oxford University Press; 1992. p. 763–773.
  • Geweke J. Evaluating the accuracy of sampling-based approaches to the calculations of posterior moments. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM, editors. Bayesian statistics 4. Oxford: Oxford University Press; 1992. p. 169–193.
  • Boone EL, Merrick JRW, Krachey MJ. A Hellinger distance approach to MCMC diagnostics. J Stat Comput Simul. 2014;84(4):833–849. doi: 10.1080/00949655.2012.729588
  • Hjorth U, Vadeby A. Subsample distribution distance and MCMC convergence. Scand J Statist. 2005;32:313–326. doi: 10.1111/j.1467-9469.2005.00424.x
  • Yu B. Estimating the L1 error of kernal estimators based on Markov samplers. UC Berkeley: 1994 (Technical Report).
  • Brooks SP, Roberts GO. Convergence assessment techniques for Markov chain Monte Carlo. Stat Comput. 1998;8(4):319–335. doi: 10.1023/A:1008820505350
  • Silverman BW. Density estimation for statistics and data analysis. London: Chapman & Hall; 1986.
  • Azzalini A, Menardi G. Clustering via nonparametric density estimation: the R package pdfCluster. J Statist Softw. 2014;57(11):1–26. doi: 10.18637/jss.v057.i11
  • Peltonen J, Venna J, Kaski S. Visualizations for assessing convergence and mixing of Markov chain Monte Carlo simulations. Comput Statist Data Anal. 2009;53(12):4453–4470. doi: 10.1016/j.csda.2009.07.001
  • Hahn T. Cuba – a library for multidimensional numerical integration. Comput Phys Comm. 2005;168(2):78–95. doi: 10.1016/j.cpc.2005.01.010
  • Bouvier A, Kiu K. R2cuba: multidimensional numerical integration; 2015; r package version 1.1-0.
  • Johnson SG, Narasimhan B. cubature: adaptive multivariate integration over hypercubes; 2013; r package version 1.1-2.
  • Leman SC, Chen Y, Lavine M. The multiset sampler. J Amer Statist Assoc. 2009;104(487):1029–1041. doi: 10.1198/jasa.2009.tm08047
  • Scheidegger A. adaptmcmc: implementation of a generic adaptive Monte Carlo Markov chain sampler; 2012; r package version 1.1.
  • Hijmans RJ, Phillips S, Leathwick J, et al. dismo: species distribution modeling; 2016; r package version 1.0-15.
  • Martin AD, Quinn KM, Park JH. MCMCpack: Markov chain Monte Carlo in R. J Statist Softw. 2011;42(9):22. doi: 10.18637/jss.v042.i09

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