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Approximating posterior distributions and posterior moments. (English) Zbl 0732.62029

Bayesian statistics 3, Proc. 3rd Valencia Int. Meet., Altea/Spain 1987, 327-344 (1988).
Summary: [For the entire collection see Zbl 0702.00028.]
A two-parameter Pearson family is fitted to univariate posterior distributions or likelihood functions by matching the first two derivatives of the log densities. This is just as easy to implement as the standard fitting of the Normal distribution. But because the Pearson families include, besides the Normal distribution, a variety of skewed and bounded or semibounded distributions (e.g., Beta, Gamma, and F distributions) there is an opportunity for improved fitting. These distributional approximations also lead to estimates of integrals (moments) that generalize the method of Laplace. When used with the Tierney-Kadane procedure [L. Tierney and J. B. Kadane, J. Am. Stat. Assoc. 81, 82-86 (1986; Zbl 0587.62067)] proposed to improve the Laplace method, they provide further improvements in the estimates of posterior moments.

MSC:

62F15 Bayesian inference
62E17 Approximations to statistical distributions (nonasymptotic)