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Bayesian Estimation of DSGE Models$
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Edward P. Herbst and Frank Schorfheide

Print publication date: 2015

Print ISBN-13: 9780691161082

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691161082.001.0001

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Combining Particle Filters with MH Samplers

Combining Particle Filters with MH Samplers

(p.218) Chapter 9 Combining Particle Filters with MH Samplers
Bayesian Estimation of DSGE Models

Edward P. Herbst

Frank Schorfheide

Princeton University Press

This chapter argues that in order to conduct Bayesian inference, the approximate likelihood function has to be embedded into a posterior sampler. It begins by combining the particle filtering methods with the MCMC methods, replacing the actual likelihood functions that appear in the formula for the acceptance probability in Algorithm 5 with particle filter approximations. The chapter refers to the resulting algorithm as PFMH algorithm. It is a special case of a larger class of algorithms called particle Markov chain Monte Carlo (PMCMC). The theoretical properties of PMCMC methods were established in Andrieu, Doucet, and Holenstein (2010). Applications of PFMH algorithms in other areas of econometrics are discussed in Flury and Shephard (2011).

Keywords:   Bayesian inference, posterior sampler, particle filtering methods, MCMC methods, PFMH algorithm, PMCMC

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