%0 Journal Article %1 vehtari2019ranknormalization %A Vehtari, Aki %A Gelman, Andrew %A Simpson, Daniel %A Carpenter, Bob %A Bürkner, Paul-Christian %D 2019 %K convergence mcmc readings sampling stats %T Rank-normalization, folding, and localization: An improved $R$ for assessing convergence of MCMC %U http://arxiv.org/abs/1903.08008 %X Markov chain Monte Carlo is a key computational tool in Bayesian statistics, but it can be challenging to monitor the convergence of an iterative stochastic algorithm. In this paper we show that the convergence diagnostic $R$ of Gelman and Rubin (1992) has serious flaws. Traditional $R$ will fail to correctly diagnose convergence failures when the chain has a heavy tail or when the variance varies across the chains. In this paper we propose an alternative rank-based diagnostic that fixes these problems. We also introduce a collection of quantile-based local efficiency measures, along with a practical approach for computing Monte Carlo error estimates for quantiles. We suggest that common trace plots should be replaced with rank plots from multiple chains. Finally, we give recommendations for how these methods should be used in practice.

@article{vehtari2019ranknormalization, abstract = {Markov chain Monte Carlo is a key computational tool in Bayesian statistics, but it can be challenging to monitor the convergence of an iterative stochastic algorithm. In this paper we show that the convergence diagnostic $\widehat{R}$ of Gelman and Rubin (1992) has serious flaws. Traditional $\widehat{R}$ will fail to correctly diagnose convergence failures when the chain has a heavy tail or when the variance varies across the chains. In this paper we propose an alternative rank-based diagnostic that fixes these problems. We also introduce a collection of quantile-based local efficiency measures, along with a practical approach for computing Monte Carlo error estimates for quantiles. We suggest that common trace plots should be replaced with rank plots from multiple chains. Finally, we give recommendations for how these methods should be used in practice.}, added-at = {2020-01-17T15:07:09.000+0100}, author = {Vehtari, Aki and Gelman, Andrew and Simpson, Daniel and Carpenter, Bob and Bürkner, Paul-Christian}, biburl = {https://www.bibsonomy.org/bibtex/23deab3ac3f4fe001b546eec8a3da7c91/kirk86}, description = {[1903.08008] Rank-normalization, folding, and localization: An improved $\widehat{R}$ for assessing convergence of MCMC}, interhash = {27525c76de16d43beffd91ffcf787fab}, intrahash = {3deab3ac3f4fe001b546eec8a3da7c91}, keywords = {convergence mcmc readings sampling stats}, note = {cite arxiv:1903.08008Comment: Revised for improved clarity}, timestamp = {2020-01-17T15:07:09.000+0100}, title = {Rank-normalization, folding, and localization: An improved $\widehat{R}$ for assessing convergence of MCMC}, url = {http://arxiv.org/abs/1903.08008}, year = 2019 }