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.

### Abstract

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.

Return to my publications page.

Updated: 24 October 2000
Maintained by: Tony O'Hagan