STA 290 Seminar Series
Thursday, February 19th, 4:10pm, MSB 1147 (Colloquium Room)
Refreshments at 3:30pm in MSB 4110 (Statistics Lounge)
Speaker: Hee Min Choi (Wald Visiting Assistant Professor, Dept Statistics, UC Davis)
Title: Analysis of MCMC algorithms for Bayesian linear regression with Laplace errors
Abstract: Let π denote the intractable posterior density that results when the standard default prior is placed on the parameters in a linear regression model with iid Laplace errors. We analyze the Markov chains under-lying two different Markov chain Monte Carlo algorithms for exploring π. In particular, it is shown that the Markov operators associated with the data augmentation (DA) algorithm and a sandwich variant are both trace-class. Consequently, both Markov chains are geometrically ergodic. It is also established that for each i Є {1, 2, 3,…}, the ith largest eigenvalue of the sandwich operator is less than or equal to the corresponding eigenvalue of the DA operator. It follows that the sandwich algorithm converges at least as fast as the DA algorithm.
(Joint work with Dr. James Hobert)