Open Access
2012 On the behaviour of Bayesian credible intervals in partially identified models
Paul Gustafson
Electron. J. Statist. 6: 2107-2124 (2012). DOI: 10.1214/12-EJS741


Partially identified models typically involve set identification rather than point identification. That is, the distribution of observables is consistent with a set of values for the target parameter, rather than a single value. Interval estimation procedures therefore behave differently than for identified models. For instance, a Bayesian credible set arising from a proper prior distribution will tend to a non-degenerate set as the sample size goes to infinity. A natural question arising is for what parameter values does the limit of the Bayesian credible interval fail to cover its target? Intuition suggests this would arise for parameter values which are not very consistent with the prior distribution. The aim of this paper is to quantify this intuition.


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Paul Gustafson. "On the behaviour of Bayesian credible intervals in partially identified models." Electron. J. Statist. 6 2107 - 2124, 2012.


Published: 2012
First available in Project Euclid: 2 November 2012

zbMATH: 1336.62102
MathSciNet: MR3020258
Digital Object Identifier: 10.1214/12-EJS741

Keywords: Bayesian inference , credible interval , partial identification

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

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