Treffer: Nested ...: Assessing the Convergence of Markov Chain Monte Carlo When Running Many Short Chains.

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 ... 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 .... This new diagnostic works under conditions similar to ... and completes the workflow for GPU-friendly samplers. In addition, the proposed nesting provides theoretical insights into the utility of ..., in both classical and short-chains regimes [ABSTRACT FROM AUTHOR]

Copyright of Bayesian Analysis is the property of International Society for Bayesian Analysis and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)