Advances and Applications in Statistics
Volume 22, Issue 1, Pages 57 - 76
(May 2011)
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A NOVEL FORMULATION FOR APPROXIMATE BAYESIAN COMPUTATION BASED ON SIGNED ROOTS OF LOG-DENSITY RATIOS
Samer A. Kharroubi and Alan Brennan
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Abstract: Based on the asymptotic theory of signed root log-density ratios, we develop some novel theory for approximate Bayesian computation. Some new accurate approximations for Bartlett corrections, posterior expectations and predictive densities are derived. These approximations are modifications of formulae based on signed root log-likelihood ratios obtained in Sweeting and Kharroubi [18], but are designed to absorb the prior into the likelihood function. This is an attractive property for various practical implications of interest, including the calculation of the expected value of sample information from decision theory. Two case study decision models from the field of health economics are used to show that the expected value of sample information approximated results are similar to the standard nested Monte Carlo sampling method, but are achieved with up to 150-fold computation time reduction. Considerably greater reductions will occur for more complex models. This new approximation formulation has wider potential benefits in many fields of Bayesian approximation. |
Keywords and phrases: signed root log-density ratio, approximate Bayesian inference, Bayesian Bartlett correction, higher-order asymptotics, Laplace approximation, predictive distribution, expected value of sample information. |
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