Particle Efficient Importance Sampling

42 Pages Posted: 27 Sep 2013

See all articles by Marcel Scharth

Marcel Scharth

The University of Sydney

Robert Kohn

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

Date Written: September 25, 2013

Abstract

The efficient importance sampling (EIS) method is a general principle for the numerical evaluation of high-dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers. Despite a number of successful applications in high dimensions, it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases. We solve this problem by recognising that the EIS framework has an offline sequential Monte Carlo interpretation. The particle EIS method is based on non-standard resampling weights that take into account the look-ahead construction of the importance sampler. We apply the method for a range of univariate and bivariate stochastic volatility specifications. We also develop a new application of the EIS approach to state space models with Student's t state innovations. Our results show that the particle EIS method strongly outperforms both the standard EIS method and particle filters for likelihood evaluation in high dimensions. Moreover, the ratio between the variances of the particle EIS and particle filter methods remains stable as the time series dimension increases. We illustrate the efficiency of the method for Bayesian inference using the particle marginal Metropolis-Hastings and importance sampling squared algorithms.

Keywords: Bayesian inference, particle filters, particle marginal Metropolis-Hastings, sequential Monte Carlo, stochastic volatility

JEL Classification: C32, C51, E43

Suggested Citation

Scharth, Marcel and Kohn, Robert, Particle Efficient Importance Sampling (September 25, 2013). Available at SSRN: https://ssrn.com/abstract=2331232 or http://dx.doi.org/10.2139/ssrn.2331232

Marcel Scharth (Contact Author)

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

HOME PAGE: http://www.marcelscharth.com

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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