C. Pereira and J. Stern have recently introduced a measure of evidence of a precise hypothesis consisting of the posterior probability of the set of points having smaller density than the supremum over the hypothesis. The related procedure is seen to be a Bayes test for specific loss functions. The nature of such loss functions and their relation to stylised inference problems are investigated. The dependence of the loss function on the sample is also discussed as well as the consequence of the introduction of Jeffrey’s prior mass for the precise hypothesis on the separability of probability and utility.
Key WordsBayesian Inference Decision Theory hypothesis test loss functions
AMS subject classification62C10 62A15 62F15 62F03
Unable to display preview. Download preview PDF.
- Good, I.J. (1988). Surprise index.Encyclopedia of Statistical Sciences,9, 104–109 (S. Kotz, N.L. Johnson and C.B. Reid, eds.) John Wiley and Sons, New York.Google Scholar
- Jeffreys, H. (1961).Theory of Probability. Oxford University Press.Google Scholar
- Pereira, C.A. de B. and J. Stern (1999). Evidence and Credibility: a full Bayesian test of precise hypothesis.Entropy 1, 104–115.Google Scholar