25 January 2024: Saifuddin Syed (University of Oxford)

Title: Scalable Bayesian inference with annealing algorithms
Abstract: Monte Carlo (MC) methods are the most widely used tools in Bayesian statistics for making inferences from complex posterior distributions. The performance of classical MC algorithms is fragile for challenging problems where the posterior is high-dimensional with well-separated modes. Annealing is a technique that adds robustness by introducing a tractable reference distribution (e.g. prior) where inference is robust and a path of distributions that continuously interpolates to the intractable poster distribution. An annealing algorithm specifies how to traverse this path to transform inferences from the reference into inferences on the target. I will show how to design and analyze a popular annealing algorithm called parallel tempering (PT), which improves the robustness of MCMC algorithms using parallel computing. I will identify near-optimal tuning guidelines for PT and an efficient black-box algorithm to implement it scalable to GPUs. Finally, I will demonstrate how to leverage the analysis of PT to establish the efficiency of a family of annealing algorithms, including annealed importance sampling and sequential Monte Carlo samplers.