Speaker:  Giulia Carigi, Postdoctoral Researcher, Department of Statistics, Indiana University

Title:  Mixing for preconditioned multiproposal MCMC algorithms

Abstract:

In this talk, we explore Markov Chain Monte Carlo (MCMC) methods for sampling high-dimensional probability measures, such as those arising in Bayesian formulations of PDE inverse problems. Our focus is on a promising class of parallel-friendly algorithms: multiproposal MCMC schemes, specifically multiproposal preconditioned Crank-Nicolson. We rigorously analyze their mixing properties in an infinite-dimensional context using the weak Harris theorem. This approach provides dimension-independent mixing rates, ensuring the algorithms are effective in high-dimensional settings.

This work is in collaboration with N. Glatt-Holtz (Indiana) and C. Mondaini (Drexel).