Topic: The Revenge of nested R-hat
Abstract: I’ll present a major revision of the nested Rhat preprint (https://arxiv.org/abs/2110.13017), with new insights on how we should reason about convergence diagnostics, and research directions for optimal MCMC (warmup and sampling) lengths. Looking for feedback!
The growing availability of hardware accelerators such as GPUs has generated interest in Markov chains Monte Carlo (MCMC) workflows which run a large number of chains in parallel. Each chain still needs to forget its initial state but the subsequent sampling phase can be almost arbitrarily short. To determine if the resulting short chains are reliable, we need to assess how close the Markov chains are to convergence to their stationary distribution. The R-hat statistic is a battle-tested convergence diagnostic but unfortunately can require long chains to work well. We present a nested design to overcome this challenge, and introduce tuning parameters to control the reliability, bias, and variance of convergence diagnostics.