Academic

This talk is about Divide-and-conquer Bayesian inference in models for dependent data. Divide-and-conquer Bayesian methods consist of three steps: dividing the data into smaller computationally manageable subsets, running a sampling algorithm in parallel on all the subsets, and combining parameter draws from all the subsets. The combined parameter draws are used for efficient posterior inference in massive data settings. Several innovative methods have been developed over the years, but a major restriction common to all of them is that their first two steps assume that the observations are independent. In this talk, we address this problem by developing a divide-and-conquer method for Bayesian inference in parametric hidden Markov models, where the state space is known and finite. First, we show that the dependence can be preserved on the subsets by appropriately modifying the subset likelihoods. Second, if the number of subsets is chosen appropriately depending on the mixing properties of the hidden Markov chain, then we show that the subset posterior distributions defined using the modified likelihood are asymptotically normal as the subset sample size tends to infinity. Finally, we present numerical results to justify the empirical validity of the theoretical results.

This presentation is based on joint work with Chunlei Wang.