A Likelihood-Free Reverse Sampler of the Posterior Distribution

Abstract

This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler approximates the likelihood-based posterior distribution by solving a sequence of simulated minimum distance problems. By a change of variable argument, these estimates are reweighted with a prior and the volume of the jacobian matrix to serve as draws from the desired posterior distribution. The sampler provides a conceptual framework to understand the difference between two types of likelihood free estimation. Because simulated minimum distance estimation always results in acceptable draws, the reverse sampler is potentially an alternative to existing approximate Bayesian methods that are computationally demanding because of a low acceptance rate.