Sequential Monte Carlo without likelihoods

doi:10.1073/pnas.0607208104

Sequential Monte Carlo without likelihoods

^†School of Mathematics and Statistics and
^§School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, NSW 2052, Australia

Edited by Michael S. Waterman, University of Southern California, Los Angeles, CA, and approved December 4, 2006 (received for review August 19, 2006)

Abstract

Recent new methods in Bayesian simulation have provided ways of evaluating posterior distributions in the presence of analytically or computationally intractable likelihood functions. Despite representing a substantial methodological advance, existing methods based on rejection sampling or Markov chain Monte Carlo can be highly inefficient and accordingly require far more iterations than may be practical to implement. Here we propose a sequential Monte Carlo sampler that convincingly overcomes these inefficiencies. We demonstrate its implementation through an epidemiological study of the transmission rate of tuberculosis.

Footnotes

^‡To whom correspondence should be addressed. E-mail: scott.sisson{at}unsw.edu.au
Author contributions: S.A.S. designed research; S.A.S. and Y.F. performed research; S.A.S. and M.M.T. contributed new reagents/analytic tools; Y.F. and M.M.T. analyzed data; and S.A.S., Y.F., and M.M.T. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS direct submission.
Abbreviations:

ABC,

approximate Bayesian computation;

MCMC,

Markov chain Monte Carlo;

PRC,

partial rejection control;

SMC,

sequential Monte Carlo;

ESS,

effective sample size.