Chan, Joshua and Eisenstat, Eric (2012): Marginal Likelihood Estimation with the CrossEntropy Method.

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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 highdimensional settings. In contrast, we use the crossentropy (CE) method, a versatile adaptive Monte Carlo algorithm originally developed for rareevent 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 in a welldefined 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.
Item Type:  MPRA Paper 

Original Title:  Marginal Likelihood Estimation with the CrossEntropy Method 
Language:  English 
Keywords:  importance sampling, model selection, probit, logit, timevarying parameter vector autoregressive model, dynamic factor model 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General 
Item ID:  40051 
Depositing User:  Joshua Chan 
Date Deposited:  13. Jul 2012 14:41 
Last Modified:  17. Feb 2013 13:14 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/40051 