Statistics Colloquium
University of Connecticut
Storrs, Connecticut
The Department of Statistics Cordially invites you to a Colloquium
Vivekananda Roy
Department of Statistics
Iowa State University
Ames, Iowa
Estimating standard errors for importance sampling
estimators with multiple Markov chains
ABSTRACT
The naive importance sampling (IS) estimator, based on samples from a single importance density, can be numerically unstable. We consider multiple distributions IS estimators where samples from more than one probability distribution are combined to consistently estimate means with respect to given target distributions. These generalized IS estimators
provide more stable estimators than naive IS estimators. We consider the Markov chain Monte Carlo context, where independent samples are replaced with Markov chains. If these Markov chains converge to their respective target distributions at a polynomial rate, then under two finite moment conditions, we show that a central limit theorem holds for the IS estimators. Further, we develop an easy to implement consistent method to calculate valid asymptotic standard errors based on the batch means (BM) methods. We also provide a BM estimator for calculating asymptotically valid standard errors of Geyer (1994)'s reverse logistic estimator. We illustrate the method with an application in Bayesian variable selection in linear regression. In particular, the multi-chain IS estimator is used to perform empirical Bayes variable selection and the BM estimator is used to obtain standard errors in the large p situation where current methods are not applicable.
DATE: Wednesday, September 23, 2015
TIME: 4:00 p.m.
PLACE: AUST 105
Coffee at 3:30 in AUST 326
For more information, contact: Tracy Burke at tracy.burke@uconn.edu