On Some Properties of Markov Chain Monte Carlo Simulation Methods Based on the Particle Filter
38 Pages Posted: 5 Jun 2019
Date Written: April 2, 2012
Andrieu et al. (2010) prove that Markov chain Monte Carlo samplers still converge to the correct posterior distribution of the model parameters when the likelihood is estimated by the particle ﬁlter (with a ﬁnite number of particles) is used instead of the likelihood. A critical issue for performance is the choice of the number of particles. We add the following contributions. First, we provide analytically derived, practical guidelines on the optimal number of particles to use. Second, we show that a fully adapted auxiliary particle ﬁlter is unbiased and can drastically decrease computing time compared to a standard particle ﬁlter. Third, we introduce a new estimator of the likelihood based on the output of the auxiliary particle ﬁlter and use the framework of Del Moral (2004) to provide a direct proof of the unbiasedness of the estimator. Fourth, we show that the results in the article apply more generally to Markov chain Monte Carlo sampling schemes with the likelihood estimated in an unbiased manner.
Keywords: Auxiliary variables; Adapted ﬁltering; Bayesian inference; Simulated likelihood
JEL Classification: C11, C15, C22
Suggested Citation: Suggested Citation