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Objective Bayes and conditional inference in exponential families

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  • Thomas J. Diciccio
  • G. Alastair Young

Abstract

Objective Bayes methodology is considered for conditional frequentist inference about a canonical parameter in a multi-parameter exponential family. A condition is derived under which posterior Bayes quantiles match the conditional frequentist coverage to a higher-order approximation in terms of the sample size. This condition is on the model, not on the prior, and it ensures that any first-order probability matching prior in the unconditional sense automatically yields higher-order conditional probability matching. Objective Bayes methods are compared to parametric bootstrap and analytic methods for higher-order conditional frequentist inference. Copyright 2010, Oxford University Press.

Suggested Citation

  • Thomas J. Diciccio & G. Alastair Young, 2010. "Objective Bayes and conditional inference in exponential families," Biometrika, Biometrika Trust, vol. 97(2), pages 497-504.
  • Handle: RePEc:oup:biomet:v:97:y:2010:i:2:p:497-504
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