Weak convergence and the exponential rate of concentration for posterior density functions

DOI10.1016/0167-7152(90)90041-5zbMath0703.62037OpenAlexW1987564841MaRDI QIDQ916255

John L. Maryak, James C. Spall

Publication date: 1990

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(90)90041-5

zbMATH Keywords

rate of convergenceexponential familyposterior densityweak convergence theoremmarginal densitiesfinite-sample resultmean value theorem for integrals

Mathematics Subject Classification ID

Multivariate analysis (62H99) Central limit and other weak theorems (60F05) Bayesian inference (62F15)

Cites Work

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• On a fundamental optimality of the maximum likelihood estimator
• The exponential rates of convergence of posterior distributions
• Conditions for the insensitivity of the Bayesian posterior distribution to the choice of prior distribution
• Asymptotic normality of the posterior distribution for exponential models
• An implicit function based procedure for analyzing maximum likelihood estimates from nonidentically distributed data
• Maximum likelihood mean and covariance matrix estimation constrained to general positive semi-definiteness
• Large sample posterior normality of the population mean
• Another Proof that Convex Functions are Locally Lipschitz
• Asymptotic Expansions Associated with Posterior Distributions

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