J. A. A. Andrade and A. O'Hagan
Federal University of Ceara, Fortaleza-Brazil and University of Sheffield
Publication details: Submitted to Annals of Statistics, 2008.
Andrade and O'Hagan (2006) used the theory of regular variation in order to address problems of conflicts (in the sense of Dawid, 1973) between the data and the prior distribution. They established sufficient conditions on the pure scale and the pure location parameter cases under which is possible to reject automatically the conflicting information. As shown by the authors, regular variation provides an easy way of understanding tails behaviour, hence the conditions needed to obtain a posterior distribution robust to conflicting information become relatively easy to verify. In this work we generalise the findings of Andrade and O'Hagan to the location-scale parameter structure. Compared with the single parameter cases, this is a much more complex structure, because of the range of conflicts that can arise between three sources of information, namely the likelihood, the prior distribution for the location parameter and the prior for the scale parameter. We establish sufficient conditions on the distributions in the location-scale model in order to resolve in different ways the conflict that arises with a single outlying observation. In each case we provide the explicit limiting form of the posterior distribution.
Keywords: Bayesian robustness, conflicting information, regularly varying distributions, RV-Credence.