Diagnostics of prior-data agreement in applied Bayesian analysis

Abstract

This article focused on the definition and the study of a binary Bayesian criterion which measures a statistical agreement between a subjective prior and data information. The setting of this work is concrete Bayesian studies. It is an alternative and a complementary tool to the method recently proposed by Evans and Moshonov, [M. Evans and H. Moshonov, Checking for Prior-data conflict, Bayesian Anal. 1 (2006), pp. 893–914]. Both methods try to help the work of the Bayesian analyst, from preliminary to the posterior computation. Our criterion is defined as a ratio of Kullback–Leibler divergences; two of its main features are to make easy the check of a hierarchical prior and be used as a default calibration tool to obtain flat but proper priors in applications. Discrete and continuous distributions exemplify the approach and an industrial case study in reliability, involving the Weibull distribution, is highlighted.

Keywords:

• prior-data conflict
• expert opinion
• subjective prior
• objective prior
• Kullback–Leibler diver-gence
• discrete distributions
• lifetime distributions

Acknowledgements

The author thanks Gilles Celeux (INRIA) and Jean-Michel Marin (INRIA) for many fruitful discussions and much advice. This study has been proposed from experimental issues by Fran\c cois Billy and Emmanuel Remy (EDF). Many thanks to Professors Christian P. Robert, Guido Consonni, Piero Veronese, Nozer D. Singpurwalla and Michael Evans for their advice, questions and comments. Finally, the author would like to thank an unknown reviewer for several comments and criticisms that greatly helped to improve the paper.

Additional information

Notes on contributors

Nicolas Bousquet

*Email: [email protected]