TITLE:

Geometric Ergodicity of Gibbs Samplers for Bayesian Mixed Models

DATE:

Friday, November 13, 2015

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Dr. Jorge Carlos Román. Assistant Professor, Statistics at SDSU

ABSTRACT:

Due to advances in Markov chain Monte Carlo (MCMC) methods, the use of Bayesian statistical models in the applied sciences has increased dramatically over the last decade. MCMC methods allow for the estimation of intractable quantities associated with complex posterior distributions. However, in a large number of applications, MCMC-based estimates are reported without a valid measure of their quality. This is largely due to the fact that it is challenging to verify that central limit theorems hold (and that there is a consistent estimator of the asymptotic variance). The standard technique for obtaining valid asymptotic standard errors for MCMC-estimates requires the Markov chain to be geometrically ergodic; that is, that the Markov chain converges to the target distribution at a geometric rate. In this talk, we consider several Bayesian versions of linear mixed models and discuss recent results that provide simple sufficient conditions for the geometric ergodicity of the associated Gibbs samplers.

HOST:

Dr. Jose Castillo

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