Marginal Likelihood Estimation with the Cross-Entropy Method

Joshua Chan and Eric Eisenstat

CAMA Working Papers from Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University

Abstract: We consider an adaptive importance sampling approach to estimating the marginal likelihood, a quantity that is fundamental in Bayesian model comparison and Bayesian model averaging. This approach is motivated by the difficulty of obtaining an accurate estimate through existing algorithms that use Markov chain Monte Carlo (MCMC) draws, where the draws are typically costly to obtain and highly correlated in high-dimensional settings. In contrast, we use the cross-entropy (CE) method, a versatile adaptive Monte Carlo algorithm originally developed for rare-event simulation. The main advantage of the importance sampling approach is that random samples can be obtained from some convenient density with little additional costs. As we are generating independent draws instead of correlated MCMC draws, the increase in simulation effort is much smaller should one wish to reduce the numerical standard error of the estimator. Moreover, the importance density derived via the CE method is grounded in information theory, and therefore, is in a well-defined sense optimal. We demonstrate the utility of the proposed approach by two empirical applications involving women’s labor market participation and U.S. macroeconomic time series. In both applications the proposed CE method compares avorably to existing estimators.

JEL-codes: C11 C15 C32 C52 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2012-05
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Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Marginal Likelihood Estimation with the Cross-Entropy Method (2015)
Working Paper: Marginal Likelihood Estimation with the Cross-Entropy Method (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:een:camaaa:2012-18

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