Contraction Properties and Computation with a Class of High-Dimensional Quasi-Posterior Distributions
Yves Atchade, University of Michigan
This talk explores a quasi-Bayesian approach to dealing with statistical models with diverging number of parameters. Some general results are described that can be used to obtain the (rate of) contraction of the resulting quasi-posterior distributions. The talk also explores a Moreau-Yosida approximation scheme that greatly facilitates Markov Chain Monte Carlo simulation from such quasi-posterior distributions. Linear regression models and Gaussian graphical models are used to illustrate the methodologies.