On bartlett adjustments for approximate Bayesian inference

Thomas J. Diciccio, Steven E. Stern

Research output: Contribution to journalArticleResearchpeer-review

25 Citations (Scopus)

Abstract

SUMMARY: In wide generality, the posterior distributions of the likehood ratio statistic and the posterior ratio statistic are chi-squared to error of order O(n -1), where n is sample size. The error in the chi-squared approximation can be reduced to order O(n -2) by Bartlett correction. In this paper, explicit formulae are derived for the Bartlett adjustment factors of both statistics, and the derivations are based on the Tierney. Kass & Kadane (1989) asymptotic approximation for marginal posterior probability density functions. The use of numerical differentiation to facilitate calculation of the Bartlett adjustments is also described. Some applications are considered that concern inference about regression models from both complete and right-censored data.

Original languageEnglish
Pages (from-to)731-740
Number of pages10
JournalBiometrika
Volume80
Issue number4
DOIs
Publication statusPublished - Dec 1993
Externally publishedYes

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Approximate Bayesian Inference
Chi-squared
Statistic
Adjustment
statistics
Bartlett Correction
Statistics
Numerical Differentiation
Right-censored Data
Posterior Probability
Asymptotic Approximation
Posterior distribution
Probability density function
Explicit Formula
Regression Model
Sample Size
Approximation
Bayesian inference
sampling

Cite this

Diciccio, Thomas J. ; Stern, Steven E. / On bartlett adjustments for approximate Bayesian inference. In: Biometrika. 1993 ; Vol. 80, No. 4. pp. 731-740.
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On bartlett adjustments for approximate Bayesian inference. / Diciccio, Thomas J.; Stern, Steven E.

In: Biometrika, Vol. 80, No. 4, 12.1993, p. 731-740.

Research output: Contribution to journalArticleResearchpeer-review

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