“Analysis of twocomponent Gibbs samplers using the theory of two projections”
featuring Dr. Qian Qin, Assistant Professor,
University of Minnesota, School of Statistics
Friday, February 18, 2022
11 a.m. – 12 p.m.
Business and Science Building, Room 132
Also available on Zoom at HTTPS://TINYURL.COM/9NRNVEUR
Abstract by Dr. Qin:
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 twocomponent Gibbs sampler can be translated into simple linear algebraic problems through Halmos’s theory. In particular, a comparison is made between the deterministicscan and randomscan versions of twocomponent Gibbs. It is found that in terms of asymptotic variance, the randomscan version is more robust than the deterministicscan version, provided that the selection probability is appropriately chosen. On the other hand, the deterministicscan version has a faster convergence rate. These results suggest that one may use the deterministicscan version in the burnin stage, and switch to the randomscan version in the estimation stage.


Date & Time
February 18, 2022
11:00 am12:00 pm
Event posted in Approved Campus Activity.