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Title: Automatic choice of driving values in Monte Carlo likelihood approximation via posterior simulations
Authors: Kuk, A.Y.C. 
Keywords: Bayesian computation
Data duplication
Generalized linear mixed models
Markov chain Monte Carlo
Missing data
Prior sharpening
Random effects
Issue Date: Apr-2003
Citation: Kuk, A.Y.C. (2003-04). Automatic choice of driving values in Monte Carlo likelihood approximation via posterior simulations. Statistics and Computing 13 (2) : 101-109. ScholarBank@NUS Repository.
Abstract: For models with random effects or missing data, the likelihood function is sometimes intractable analytically but amenable to Monte Carlo approximation. To get a good approximation, the parameter value that drives the simulations should be sufficiently close to the maximum likelihood estimate (MLE) which unfortunately is unknown. Introducing a working prior distribution, we express the likelihood function as a posterior expectation and approximate it using posterior simulations. If the sample size is large, the sample information is likely to outweigh the prior specification and the posterior simulations will be concentrated around the MLE automatically, leading to good approximation of the likelihood near the MLE. For smaller samples, we propose to use the current posterior as the next prior distribution to make the posterior simulations closer to the MLE and hence improve the likelihood approximation. By using the technique of data duplication, we can simulate from the sharpened posterior distribution without actually updating the prior distribution. The suggested method works well in several test cases. A more complex example involving censored spatial data is also discussed.
Source Title: Statistics and Computing
ISSN: 09603174
DOI: 10.1023/A:1023248207299
Appears in Collections:Staff Publications

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