Recent developments of Monte Carlo sampling strategies for probability distributions on submanifolds

Abstract: Monte Carlo sampling for probability distributions on submanifolds is involved in many applications in molecular dynamics, statistical mechanics and Bayesian computation. In this talk, I will talk about two types of Monte Carlo schemes that are developed in recent years. The first type of schemes is based on the ergodicity of stochastic differential equations (SDEs) on submanifolds and is asymptotically unbiased as the step-size vanishes. The second type of schemes consists of Markov chain Monte Carlo (MCMC) algorithms that are unbiased when finite step-sizes are used. I will discuss the role of projections onto submanifolds, as well as the necessity of the so-called "reversibility check'' step in MCMC schemes on submanifolds that is first pointed out by Goodman, Holmes-Cerfon and Zappa. During the talk, I will illustrate both types of schemes with some numerical examples.

Computer scienceMathematicsPhysics

Audience: researchers in the topic

Data Science and Computational Statistics Seminar