Leitura do Dia - Bayesian heavy-tailed models and conflict resolution: a review
Anthony OHagan and Luis Pericchi
April 5, 2011
We review a substantial literature, spanning 50 years, concerning the resolution of conflicts using Bayesian heavy-tailed models. Conicts arise when different sources of information about the model parameters (e.g. prior information, or the information in individual observations) sug-
gest quite different plausible regions for those parameters. Traditional Bayesian models based on normal distributions or other conjugate structures typically resolve conicts by centring the posterior at some compromise position, but this is not a realistic resolution when it means that
the posterior is then in conict with the different information sources.
Bayesian modelling with heavy-tailed distributions has been shown to produce more reasonable conict resolution, typically by favouring one source of information over the other. The less favoured source is ultimately wholly or partially rejected as the conict becomes increasingly
The literature reviewed here provides formal proofs of conict resolution by asymptotic rejection of some information sources. Results are given for a variety of models, from the simplest case of a single observation relating to a single location parameter up to models with many
location parameters, location and scale parameters, or other kinds of parameters. However, these results do not begin to address models of the kind of complexity that are routinely used in practical Bayesian modelling. In addition to reviewing the available theory, we also identify clearly the gaps in the literature that need to be filled in order for modellers to be able to develop applications with appropriate built-in robustness.
Keywords: rejection of information, partial rejection of information, built-in robustness, heavy-tailed modelling, theory of confflict resolution,