Markov Interacting Importance Samplers

44 Pages Posted: 26 Feb 2015 Last revised: 25 Jun 2015

See all articles by Eduardo F Mendes

Eduardo F Mendes

UNSW Australia Business School, School of Economics

Marcel Scharth

The University of Sydney

Robert Kohn

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

Date Written: June 25, 2015


We introduce a new Markov chain Monte Carlo (MCMC) sampler called the Markov Interacting Importance Sampler (MIIS). The MIIS sampler uses conditional importance sampling (IS) approximations to jointly sample the current state of the Markov Chain and estimate conditional expectations, possibly by incorporating a full range of variance reduction techniques. We compute Rao-Blackwellized estimates based on the conditional expectations to construct control variates for estimating expectations under the target distribution. The control variates are particularly efficient when there are substantial correlations between the variables in the target distribution, a challenging setting for MCMC. An important motivating application of MIIS occurs when the exact Gibbs sampler is not available because it is infeasible to directly simulate from the conditional distributions. In this case the MIIS method can be more efficient than a Metropolis-within-Gibbs approach. We also introduce the MIIS random walk algorithm, designed to accelerate convergence and improve upon the computational efficiency of standard random walk samplers. Simulated and empirical illustrations for Bayesian analysis show that the method significantly reduces the variance of Monte Carlo estimates compared to standard MCMC approaches, at equivalent implementation and computational effort.

Keywords: Bayesian inference, Control variates, Mixed Logit, PMCMC, Markov Modulated Poisson Process, Rao-Blackwellization, Variance reduction

JEL Classification: C15

Suggested Citation

Mendes, Eduardo Fonseca and Scharth, Marcel and Kohn, Robert, Markov Interacting Importance Samplers (June 25, 2015). Available at SSRN: or

Eduardo Fonseca Mendes

UNSW Australia Business School, School of Economics ( email )

High Street
Sydney, NSW 2052

Marcel Scharth (Contact Author)

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006


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
+61 2 9385 2150 (Phone)

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