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Some new formulae for posterior expectations and Bartlett corrections. (English) Zbl 1044.62034

Summary: Some new accurate approximations for posterior expectations and Bartlett corrections are derived. These approximations are modifications of formulae based on signed root log-likelihood ratios obtained by T. J. Sweeting [J. M. Bernardo et al. (eds.), Bayesian Statistics 5, 427–444 (1996)] and are designed to address two problems that arise in the practical application of these formulae in the multiparameter case. The first problem is a computational one associated with inversion of signed root log-likelihood ratios. The second concerns the form of the posterior expectation formula, which is not in a particularly convenient form for the computation of predictive densities. The theory is illustrated by two examples.

MSC:

62F15 Bayesian inference
62E20 Asymptotic distribution theory in statistics
62F25 Parametric tolerance and confidence regions
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