Estimating Standard Errors for Importance Sampling Estimators with Multiple Markov Chains

• Activity Number: 524
• Type: Topic Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Vivekananda Roy* and Aixin Tan and James M. Flegal
• Companies: Iowa State University and The University of Iowa and UC Riverside
• Keywords: Geometric ergodicity ; Importance sampling ; Markov chain Monte Carlo ; standard errors

Abstract

The naive importance sampling estimator based on the samples from a single importance density can be extremely numerically unstable. We consider multiple distributions importance sampling estimators where samples from more than one probability distributions are combined to consistently estimate means with respect to a given target distribution. These generalized importance sampling estimators provide more stable estimators than the naive importance sampling estimators. Importance sampling estimators can also be used in the Markov chain Monte Carlo (MCMC) context, that is, where iid samples are replaced with Harris ergodic Markov chains with invariant importance distributions. Recently Tan Doss and Hobert (2014) developed an approach based on regenerative simulation for calculating standard errors of these importance sampling estimators. It is well-known that in practice it is often difficult to construct a useful minorization condition that is required in Tan Doss and Hobert's (2014) regenerative simulation method. We provide an alternative estimator for these standard errors based on the easy to implement batch means methods.