Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of MCMC (with Discussion)

@article{Vehtari2020RankNormalizationFA,
  title={Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of MCMC (with Discussion)},
  author={Aki Vehtari and Andrew Gelman and Daniel P. Simpson and Bob Carpenter and Paul-Christian Burkner},
  journal={Bayesian Analysis},
  year={2020}
}
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… 
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