The Gibbs Sampler with Particle Efficient Importance Sampling for State-Space Models

43 Pages Posted: 7 Jan 2016 Last revised: 22 Feb 2017

See all articles by Oliver Grothe

Oliver Grothe

KIT

Tore Selland Kleppe

University of Stavanger

Roman Liesenfeld

University of Cologne, Department of Economics

Date Written: February 20, 2017

Abstract

We consider Particle Gibbs (PG) as a tool for Bayesian analysis of non-linear non-Gaussian state-space models. PG is a Monte Carlo (MC) approximation of the standard Gibbs procedure which uses sequential MC (SMC) importance sampling inside the Gibbs procedure to update the latent and potentially high-dimensional state trajectories. We propose to combine PG with a generic and easily implementable SMC approach known as Particle Efficient Importance Sampling (PEIS). By using SMC importance sampling densities which are approximately fully globally adapted to the targeted density of the states, PEIS can substantially improve the mixing and the efficiency of the PG draws from the posterior of the states and the parameters relative to existing PG implementations.The efficiency gains achieved by PEIS are illustrated in PG applications to a univariate stochastic volatility model for asset returns, a Gaussian nonlinear local-level model for interest rates, and a multivariate stochastic volatility model for the realized covariance matrix of asset returns.

Keywords: Ancestor sampling, Dynamic latent variable models, Efficient importance sampling, Markov chain Monte Carlo, Sequential importance sampling

JEL Classification: C11, C13, C15, C22

Suggested Citation

Grothe, Oliver and Kleppe, Tore Selland and Liesenfeld, Roman, The Gibbs Sampler with Particle Efficient Importance Sampling for State-Space Models (February 20, 2017). Available at SSRN: https://ssrn.com/abstract=2711296 or http://dx.doi.org/10.2139/ssrn.2711296

Oliver Grothe

KIT ( email )

Kaiserstraße 12
Karlsruhe, Baden Württemberg 76131
Germany

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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