Application of a predictive distribution formula to Bayesian computation for incomplete data models |
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Authors: | Trevor Sweeting Samer Kharroubi |
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Institution: | (1) University College London and University of Sheffield, UK |
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Abstract: | We consider exact and approximate Bayesian computation in the presence of latent variables or missing data. Specifically we explore the application of a posterior predictive distribution formula derived in Sweeting And Kharroubi (2003), which is a particular form of Laplace approximation, both as an importance function and a proposal distribution. We show that this formula provides a stable importance function for use within poor man’s data augmentation schemes and that it can also be used as a proposal distribution within a Metropolis-Hastings algorithm for models that are not analytically tractable. We illustrate both uses in the case of a censored regression model and a normal hierarchical model, with both normal and Student t distributed random effects. Although the predictive distribution formula is motivated by regular asymptotic theory, it is not necessary that the likelihood has a closed form or that it possesses a local maximum. |
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Keywords: | asymptotic approximation Bayesian computation data augmentation importance sampling Laplace approximation latent variables Metropolis-Hastings missing data predictive distribution simulation |
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