The Department of Mathematical Sciences will host Dr. Qian Qin, Assistant Professor of Statistics at the University of Minnesota, for its math seminar series. Dr. Qin will present, “Analysis of two-component Gibbs samplers using the theory of two projections.” This free seminar will take place on Friday, February 18, at 11 a.m. in BSB 132. A virtual option is also available: https://tinyurl.com/9nrnveur.
Gibbs samplers are a class of Markov chain Monte Carlo (MCMC) algorithms commonly used in statistics for sampling from intractable probability distributions. In this talk, I will demonstrate how Halmos’s (1969) theory of two projections can be applied to study Gibbs samplers with two components. I will first give an introduction to MCMC algorithms, particularly Gibbs algorithms. Then, I will explain how problems regarding the asymptotic variance and convergence rate of a two-component Gibbs sampler can be translated into simple linear algebraic problems through Halmos’s theory. In particular, a comparison is made between the deterministic-scan and random-scan versions of two-component Gibbs. It is found that in terms of asymptotic variance, the random-scan version is more robust than the deterministic-scan version, provided that the selection probability is appropriately chosen. On the other hand, the deterministic-scan version has a faster convergence rate. These results suggest that one may use the deterministic-scan version in the burn-in stage, and switch to the random-scan version in the estimation stage.