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CD posterior – combining prior and data through confidence distributions
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.
First available in Project Euclid: 14 March 2012
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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
Copyright © 2012, Institute of Mathematical Statistics
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. https://projecteuclid.org/euclid.imsc/1331731621
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