Higher Order Expansions for Posterior Distributions Using Posterior Modes

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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Bibliographische Detailangaben
Veröffentlicht in:JOURNAL OF THE JAPAN STATISTICAL SOCIETY 2009/02/24, Vol.38(3), pp.415-429
1. Verfasser: Miyata, Yoichi
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic expansion
Bayesian inference
Laplace's method
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Beschreibung
Zusammenfassung: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