Bayesian Analysis· 2020Q1
Rank-Normalization, Folding, and Localization: An Improved Rˆ for Assessing Convergence of MCMC (with Discussion)
- 1,539citations
- Q1SCImago
- 2020year
Short summary
A new rank-based diagnostic, Rˆ, is proposed to fix flaws in the traditional Gelman-Rubin Rˆ, accurately assessing Markov chain Monte Carlo (MCMC) convergence even with heavy tails or varying variances across chains.
AI-generated from the title and abstract; the full text is not read.
Key points
- Traditional Gelman-Rubin Rˆ diagnostic fails with heavy-tailed MCMC or varying variances.
- A new rank-based diagnostic, Rˆ, is proposed to address these convergence assessment failures.
- The paper introduces quantile-based local efficiency measures and methods for Monte Carlo error estimation.
- Rank plots from multiple chains are recommended as a replacement for common trace plots.
AI-generated from the title and abstract; the full text is not read.
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 Rˆ of Gelman and Rubin (1992) has serious flaws. Traditional Rˆ 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.
The authors' abstract, as published at the source. Bayesian Analysis, 2020 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics