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Nested R: Assessing the Convergence of Markov Chain Monte Carlo When Running Many Short Chains
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en
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28
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Bayesian Analysis, Volume 20, issue 4, pp. 1587-1614
Abstract
Recent developments in parallel Markov chain Monte Carlo (MCMC) algorithms allow us to run thousands of chains almost as quickly as a single chain, using hardware accelerators such as GPUs. While each chain still needs to forget its initial point during a warmup phase, the subsequent sampling phase can be shorter than in classical settings, where we run only a few chains. To determine if the resulting short chains are reliable, we need to assess how close the Markov chains are to their stationary distribution after warmup. The potential scale reduction factor (R) over cap is a popular convergence diagnostic but unfortunately can require a long sampling phase to work well. We present a nested design to overcome this challenge and a generalization called nested (R) over cap. This new diagnostic works under conditions similar to (R) over cap and completes the workflow for GPU-friendly samplers. In addition, the proposed nesting provides theoretical insights into the utility of (R) over cap, in both classical and short-chains regimes.
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Margossian, C C, Hoffman, M D, Sountsov, P, Riou-Durand, L, Vehtari, A & Gelman, A 2025, 'Nested R: Assessing the Convergence of Markov Chain Monte Carlo When Running Many Short Chains', Bayesian Analysis, vol. 20, no. 4, pp. 1587-1614. https://doi.org/10.1214/24-BA1453