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CD posterior – combining prior and data through confidence distributions

Kesar Singh and Minge Xie

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Abstract

This article proposes an alternative approach to incorporate information from observed data with its corresponding prior information using a recipe developed for combining confidence distributions. The outcome function is called a CD posterior, an alternative to Bayes posterior, which is shown here to have the same coverage property as the Bayes posterior. This approach to incorporating a prior distribution has a great advantage that it does not require any prior on nuisance parameters. It also can ease the computational burden which a typical Bayesian analysis endures. An error bound is established on the CD-posterior when there is an error in prior specification.

Chapter information

Source
Dominique Fourdrinier, Éric Marchand and Andrew L. Rukhin, eds., Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2012), 200-214

Dates
First available: 14 March 2012

Permanent link to this document
http://projecteuclid.org/euclid.imsc/1331731621

Digital Object Identifier
doi:10.1214/11-IMSCOLL814

Subjects
Primary: 62A01: Foundations and philosophical topics 62F03: Hypothesis testing 62F12: Asymptotic properties of estimators 62F15: Bayesian inference 62F40: Bootstrap, jackknife and other resampling methods 62G05: Estimation 62G10: Hypothesis testing 62G20: Asymptotic properties

Keywords
posterior distribution confidence distribution frequentist coverage

Citation

Singh, Kesar; Xie, Minge. CD posterior – combining prior and data through confidence distributions. Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman, 200--214, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2012. doi:10.1214/11-IMSCOLL814. http://projecteuclid.org/euclid.imsc/1331731621.


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