Marginal likelihood estimation with the cross-entropy method

Chan, Joshua C. C. and Eisenstat, Eric (2015) Marginal likelihood estimation with the cross-entropy method. Econometric Reviews, 34 3: 256-285. doi:10.1080/07474938.2014.944474

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Author Chan, Joshua C. C.
Eisenstat, Eric
Title Marginal likelihood estimation with the cross-entropy method
Journal name Econometric Reviews   Check publisher's open access policy
ISSN 0747-4938
Publication date 2015-01-01
Sub-type Article (original research)
DOI 10.1080/07474938.2014.944474
Open Access Status Not Open Access
Volume 34
Issue 3
Start page 256
End page 285
Total pages 30
Place of publication New York, NY, United States
Publisher Taylor & Francis
Language eng
Formatted 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 favorably to existing estimators.
Keyword Dynamic factor model
Importance sampling
Model selection
Time-varying parameter vector autoregressive model
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Non HERDC
School of Economics Publications
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Citation counts: TR Web of Science Citation Count  Cited 9 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 9 times in Scopus Article | Citations
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Created: Sun, 24 Jan 2016, 00:25:59 EST by Eric Eisenstat on behalf of School of Economics