Using simulation to handle implicit likelihoods in a Bayesian analysis

KEY POINTS

This article presents a Bayesian inferential method where the likelihood for a model is unknown, i.e., an implicit likelihood, but where data can easily be simulated from the data model. We use simulated data to estimate the implicit likelihood in a Bayesian analysis employing a Markov chain Monte Carlo algorithm. Two examples are presented.

About the author

M. S. Hamada received a Ph.D. in Statistics from the University of Wisconsin-Madison. T. L. Graves received a Ph.D. in Statistics from Stanford University. N. W. Hengartner received a Ph.D. in Statistics from the University of California-Berkeley. D. M. Higdon received a Ph.D. in Statistics from the University of Washington. A. V. Huzurbazar received a Ph.D. in Statistics from Colorado State University. E. Lawrence received a Ph.D. in Statistics from the University of Michigan. C. D. Linkletter received a Ph.D. in Statistics from Simon Fraser University. C. S. Reese received a Ph.D. in Statistics from Texas A & M. D. W. Scott received a Ph.D. in Statistics from Rice University. R. R. Sitter received a Ph.D. in Statistics from the University of Waterloo. R. L. Warr received a Ph.D. in Statistics from the University of New Mexico. B. J. Williams received a Ph.D. in Statistics from The Ohio State University.

Acknowledgments

We thank C. C. Essix for her encouragement and support. We thank Brian Weaver for his helpful comments on an earlier version. This article is dedicated to the memory of Randy Sitter, our dear colleague, mentor, and friend.