2021/07/22 by Quan Zhou, Aaron Smith, Zhou, Quan +1 · 1 citation
Mathematics · #60J10 #60J20 #60J27 #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2107.10827
openalex publication_date 2021/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Informed Markov chain Monte Carlo (MCMC) methods have been proposed as scalable solutions to Bayesian posterior computation on high-dimensional discrete state spaces, but theoretical results about their convergence behavior in general settings are lacking. In this article, we propose a class of MCMC schemes called informed importance tempering (IIT), which combine importance sampling and informed local proposals, and derive generally applicable spectral gap bounds for IIT estimators. Our theory shows that IIT samplers have remarkable scalability when the target posterior distribution concentrates on a small set. Further, both our theory and numerical experiments demonstrate that the informed proposal should be chosen with caution: the performance of some proposals may be very sensitive to the shape of the target distribution. We find that the "square-root proposal weighting" scheme tends to perform well in most settings.