Annals of the Institute of Statistical Mathematics vol:65 issue:3 pages:491-511
In the Bayesian modelling the data and the prior information concerning a certain parameter of interest may conflict, in the sense that the information carried
by them disagree. The most common form of conflict is the presence of outlying information in the data, which may potentially lead to wrong posterior conclusions.
To prevent this problem we use robustmodels which aim to control the influence of the atypical information in the posterior distribution. Roughly speaking, we conveniently
use heavy-tailed distributions in the model in order to resolve conflicts in favour of those sources of information which we believe is more credible. The class of heavytailed
distributions is quite wide and the literature have been concerned in establishing conditions on the data and prior distributions in order to reject the outlying information.
In thiswork we focus on the subexponential andLclasses of heavy-tailed distributions, in which we establish sufficient conditions under which the posterior distribution
automatically rejects the conflicting information.