Importance Sampling Squared for Bayesian Inference in Latent Variable Models

39 Pages Posted: 28 Jan 2014

See all articles by Minh-Ngoc Tran

Minh-Ngoc Tran

UNSW Business School

Marcel Scharth

The University of Sydney

Michael K. Pitt

University of Warwick

Robert Kohn

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

Date Written: January 25, 2014

Abstract

We consider Bayesian inference by importance sampling when the likelihood is analytically intractable but can be unbiasedly estimated. We refer to this procedure as importance sampling squared (IS2), as we can often estimate the likelihood itself by importance sampling. We provide a formal justification for importance sampling when working with an estimate of the likelihood and study its convergence properties. We analyze the effect of estimating the likelihood on the resulting inference and provide guidelines on how to set up the precision of the likelihood estimate in order to obtain an optimal tradeoff between computational cost and accuracy for posterior inference on the model parameters. We illustrate the procedure in empirical applications for a generalized multinomial logit model and a stochastic volatility model. The results show that the IS2 method can lead to fast and accurate posterior inference under the optimal implementation.

Keywords: Efficient importance sampling, marginal likelihood, multinomial logit, particle marginal Metropolis-Hastings, optimal number of particles, stochastic volatility

JEL Classification: C32, C51, E43

Suggested Citation

Tran, Minh-Ngoc and Scharth, Marcel and Pitt, Michael K. and Kohn, Robert, Importance Sampling Squared for Bayesian Inference in Latent Variable Models (January 25, 2014). Available at SSRN: https://ssrn.com/abstract=2386371 or http://dx.doi.org/10.2139/ssrn.2386371

Minh-Ngoc Tran

UNSW Business School ( email )

UNSW Business School
High St
Sydney, NSW 2052
Australia

Marcel Scharth (Contact Author)

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

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

Michael K. Pitt

University of Warwick ( email )

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

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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