Sequential Monte Carlo without likelihoods

• DOI: 10.1073/pnas.0607208104
• Publication Date: 2007-02-02T22:47:54Z
• Authors: S. A. Sisson; Y. Fan; Mark M. Tanaka
• Keywords: sampling; Likelihood Functions; Models, Statistical; 330; Bayesian inference; Bayes Theorem; intractable likelihoods; 01 natural sciences; approximate Bayesian computation; importance; tuberculosis; Animals; Humans; Tuberculosis; Computer Simulation; 0101 mathematics; Monte Carlo Method; Algorithms

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.