Higher Order Expansions for Posterior Distributions Using Posterior Modes

The (arbitrary) higher order asymptotic expansion for posterior distributions of a single parameter is derived by using posterior modes, and its validity is shown. An asymptotic expansion for the Bayes risk with squared error loss of a posterior mode is derived.

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Bibliographic Details
Published inJOURNAL OF THE JAPAN STATISTICAL SOCIETY Vol. 38; no. 3; pp. 415 - 429
Main Author Miyata, Yoichi
Format Journal Article
LanguageEnglish
Published Tokyo THE JAPAN STATISTICAL SOCIETY 01.01.2008
Japan Science and Technology Agency
Subjects
Asymptotic expansion
Bayesian inference
Laplace's method
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Summary:The (arbitrary) higher order asymptotic expansion for posterior distributions of a single parameter is derived by using posterior modes, and its validity is shown. An asymptotic expansion for the Bayes risk with squared error loss of a posterior mode is derived.
ISSN:1882-2754
1348-6365
DOI:10.14490/jjss.38.415