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Asymptotic approximations to posterior distributions via conditional moment equations

Biometrika

By:
, , and
DOI: 10.1093/biomet/89.4.755

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Abstract

We consider asymptotic approximations to joint posterior distributions in situations where the full conditional distributions referred to in Gibbs sampling are asymptotically normal. Our development focuses on problems where data augmentation facilitates simpler calculations, but results hold more generally. Asymptotic mean vectors are obtained as simultaneous solutions to fixed point equations that arise naturally in the development. Asymptotic covariance matrices flow naturally from the work of Arnold & Press (1989) and involve the conditional asymptotic covariance matrices and first derivative matrices for conditional mean functions. When the fixed point equations admit an analytical solution, explicit formulae are subsequently obtained for the covariance structure of the joint limiting distribution, which may shed light on the use of the given statistical model. Two illustrations are given. ?? 2002 Biometrika Trust.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Asymptotic approximations to posterior distributions via conditional moment equations
Series title:
Biometrika
DOI:
10.1093/biomet/89.4.755
Volume
89
Issue:
4
Year Published:
2002
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Biometrika
First page:
755
Last page:
767