Sequential Monte Carlo without likelihoods

Sequential Monte Carlo without likelihoods

February 6, 2007 | S. A. Sisson†‡, Y. Fan†, and Mark M. Tanaka§
The paper introduces a sequential Monte Carlo (SMC) sampler for approximate Bayesian computation (ABC), which is designed to overcome the inefficiencies of existing ABC methods such as rejection sampling and Markov chain Monte Carlo (MCMC). The SMC sampler propagates a population of particles through a sequence of intermediary distributions, gradually moving towards the target distribution. This approach ensures that the sampler never gets "stuck" in regions of low probability, unlike MCMC, and avoids the inefficiency of rejection sampling. The authors demonstrate the effectiveness of their method through a toy example and a reanalysis of a study on tuberculosis transmission rates, showing that their ABC-PRC algorithm is significantly more efficient than both ABC-MCMC and ABC-rejection sampling. The paper also discusses the advantages and disadvantages of the SMC approach and provides a detailed algorithm for the ABC-PRC sampler.The paper introduces a sequential Monte Carlo (SMC) sampler for approximate Bayesian computation (ABC), which is designed to overcome the inefficiencies of existing ABC methods such as rejection sampling and Markov chain Monte Carlo (MCMC). The SMC sampler propagates a population of particles through a sequence of intermediary distributions, gradually moving towards the target distribution. This approach ensures that the sampler never gets "stuck" in regions of low probability, unlike MCMC, and avoids the inefficiency of rejection sampling. The authors demonstrate the effectiveness of their method through a toy example and a reanalysis of a study on tuberculosis transmission rates, showing that their ABC-PRC algorithm is significantly more efficient than both ABC-MCMC and ABC-rejection sampling. The paper also discusses the advantages and disadvantages of the SMC approach and provides a detailed algorithm for the ABC-PRC sampler.
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[slides and audio] Sequential Monte Carlo without likelihoods