Statistics Department Seminar Series: Galin Jones, Professor of Statistics, University of Minnesota

Abstract:

It is common practice in Markov chain Monte Carlo to update the simulation one variable (or block of variables) at a time, rather than conduct a single full-dimensional update. When it is possible to draw from each full-conditional distribution associated with the target this is just a Gibbs sampler. Often at least one of the Gibbs updates is replaced with a Metropolis–Hastings step, yielding a Conditional Metropolis–Hastings algorithm. Strategies for combining component-wise updates include composition, random sequence and random scans. While these strategies can ease MCMC implementation and produce superior empirical performance compared to full-dimensional updates, the theoretical convergence properties of the associated Markov chains have received limited attention. I will present some recent results on the convergence properties of component-wise MCMC methods, paying particular attention to connections between various algorithms. The connection between the theory and methods for implementing MCMC reliably will be emphasized.

This seminar will be livestreamed via Zoom https://umich.zoom.us/j/94350208889
There will be a virtual reception to follow.