On Some Properties of Markov Chain Monte Carlo Simulation Methods Based on the Particle Filter

38 Pages Posted: 5 Jun 2019

See all articles by Michael K. Pitt

Michael K. Pitt

University of Warwick

Ralph Silva

Universidade Federal do Rio de Janeiro (UFRJ)

Paolo Giordani

Norwegian Business School

Robert Kohn

University of New South Wales - School of Economics and School of Banking and Finance

Date Written: April 2, 2012

Abstract

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

Pitt, Michael K. and Silva, Ralph and Giordani, Paolo and Kohn, Robert, On Some Properties of Markov Chain Monte Carlo Simulation Methods Based on the Particle Filter (April 2, 2012). Journal of Econometrics, Vol. 171, No. 2, 2012, UNSW Business School Research Paper Forthcoming, Available at SSRN: https://ssrn.com/abstract=3389761

Michael K. Pitt

University of Warwick ( email )

Gibbet Hill Rd.
Coventry, West Midlands CV4 8UW
United Kingdom

Ralph Silva

Universidade Federal do Rio de Janeiro (UFRJ) ( email )

Av; Pasteur, 250
terreo - Bairro Maracana
Rio de Janeiro, Rio de Janeiro 23890000
Brazil

Paolo Giordani (Contact Author)

Norwegian Business School ( email )

Nydalsveien 37
Oslo, 0442
Norway

Robert Kohn

University of New South Wales - School of Economics and School of Banking and Finance ( email )

Australian School of Business
Sydney NSW 2052, ACT 2600
Australia
+61 2 9385 2150 (Phone)

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