University of Sheffield

Tony O'Hagan - Academic pages - Abstracts


Sensitivity of the Fractional Bayes Factor to Prior Distributions

C. Conigliani and A. O'Hagan

University of Roma Tre and University of Sheffield

Publication details: Canadian Journal of Statistics 28, 343-352, 2000.


Calculation of a suitable Bayes factor is required for Bayesian model comparison. In recent years, several alternative Bayes factors have been introduced to address the problem of sensitivity of the usual Bayes factor when prior information is weak. Among these alternatives, the fractional Bayes factor makes an important contribution, on the grounds of consistency, robustness and coherence.

Sensitivity of the fractional Bayes factor with respect to prior distributions is easy to assess when these are proper. On the other hand, when the priors are improper, most methods lead to trivial answers. Also, earlier work on fractional Bayes factors has assumed that sensitivity will be reduced if the training fraction, b, is increased, but this has only been justified by appeal to heuristic reasoning and simple examples. In this paper we derive a measure of the sensitivity of the fractional Bayes factor with respect to improper priors, and prove that it is a decreasing function of b in a class of problems.

Keywords: fractional Bayes factor, sensitivity, Gateaux differential, improper priors, training sample.

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Updated: 24 October 2000
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