Seminar in applied mathematics and statistics

SPEAKER: Jes Frellsen

TITLE: Bayesian generalized ensemble Markov chain Monte Carlo

ABSTRACT:
The Markov chain Monte Carlo method is one of the most important tools for approximate inference for high dimensional models. However, in many applications the Markov chain can suffer from slow convergence and poor mixing. The so-called generalized ensemble method can potentially alleviate this problem by constructing a new Markov chain that simulates a random walk between different values of the log likelihood function.

Subsequently estimates for partition functions (marginal likelihood or evidence) can be obtained by reweighting. The main challenge in applying generalized ensembles is that one has to solve an inference problem on the density of states. Here we present a Bayesian approach to solving this inference problem using a Gaussian process prior for the density of states. As a proof of concept we present results on calculating partition functions for Ising and Potts models.