Qian Qin, University of Minnesota

Qian Qin, University of Minnesota  

Spectral gap decomposition for Markov chains with application  to hybrid Gibbs samplers

ABSTRACT 

Hybrid Gibbs samplers represent a prominent class of approximated Gibbs algorithms that utilize Markov chains to approximate conditional distributions, with the Metropolis-within-Gibbs algorithm standing out as a well-known example. Despite their widespread use in both statistical and non-statistical applications, little is known about their convergence properties. In this talk, I will describe a new type of bound on the convergence rates of  hybrid random-scan Gibbs algorithms. It is shown that the spectral gap of a hybrid Gibbs chain can be bounded based on the spectral gap of the ideal Gibbs chain and the spectral gaps of the Markov chains employed for conditional distribution approximations. 
 

BIO

Qian Qin is an Assistant Professor of Statistics at the University of Minnesota. He obtained his Ph.D. from the University of Florida under the supervision of James Hobert. His research revolves around Markov chain theory and the analysis of Markov chain Monte Carlo algorithms.