Pseudo-Marginal Hamiltonian Monte Carlo with Efficient Importance Sampling

29 Pages Posted: 3 Jan 2019

See all articles by Kjartan Kloster Osmundsen

Kjartan Kloster Osmundsen

University of Stavanger - Department of Mathematics and Physics

Tore Selland Kleppe

University of Stavanger

Roman Liesenfeld

University of Cologne, Department of Economics

Date Written: December 19, 2018

Abstract

The joint posterior of latent variables and parameters in Bayesian hierarchical models often has a strong nonlinear dependence structure, thus making it a challenging target for standard Markov-chain Monte-Carlo methods. Pseudo-marginal methods aim at effectively exploring such target distributions, by marginalizing the latent variables using Monte-Carlo integration and directly targeting the marginal posterior of the parameters. We follow this approach and propose a generic pseudo-marginal algorithm for efficiently simulating from the posterior of the parameters. It combines efficient importance sampling, for accurately marginalizing the latent variables, with the recently developed pseudo-marginal Hamiltonian Monte Carlo approach. We illustrate our algorithm in applications to dynamic state space models, where it shows a very high simulation efficiency even in challenging scenarios with complex dependence structures.

Keywords: Hamiltonian Monte Carlo, Efficient Importance Sampling, Bayesian Hierarchical Models, State Space Models

JEL Classification: C11, C13, C14, C20, C22

Suggested Citation

Kloster Osmundsen, Kjartan and Kleppe, Tore Selland and Liesenfeld, Roman, Pseudo-Marginal Hamiltonian Monte Carlo with Efficient Importance Sampling (December 19, 2018). Available at SSRN: https://ssrn.com/abstract=3304077 or http://dx.doi.org/10.2139/ssrn.3304077

Kjartan Kloster Osmundsen

University of Stavanger - Department of Mathematics and Physics ( email )

Norway

Tore Selland Kleppe

University of Stavanger ( email )

PB 8002
Stavanger, 4036
Norway

Roman Liesenfeld (Contact Author)

University of Cologne, Department of Economics ( email )

Albertus-Magnus-Platz
D-50931 Köln
Germany

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