## Special Colloquium

### Friday, January 25th, 2019

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Qian Qin (University of Florida)

**Title:** Convergence complexity analysis of MCMC.

**Abstract: ** Convergence complexity analysis is the study of how Markov chain Monte Carlo (MCMC) algorithms used in Bayesian statistics scale with the size of the underlying data set. To conduct this type of analysis, one needs tools to construct convergence bounds for high-dimensional Markov chains. I will review a few classical techniques of Markov chain convergence analysis (in particular, drift and minorization), and discuss their applicability and limitations in high-dimensional settings. I will then present a result concerning the convergence complexity of Albert and Chib's algorithm for Bayesian probit regression.

**Qian Qin** is a Ph.D. Candidate in Statistics at the University of Florida. His research interests include Markov chain Monte Carlo, Bayesian statistics, and high-dimensional statistics.