Brazilian Journal of Probability and Statistics

Bayesian heavy-tailed models and conflict resolution: A review

Anthony O’Hagan and Luis Pericchi

Full-text: Open access

Abstract

We review a substantial literature, spanning 50 years, concerning the resolution of conflicts using Bayesian heavy-tailed models. Conflicts arise when different sources of information about the model parameters (e.g., prior information, or the information in individual observations) suggest quite different plausible regions for those parameters. Traditional Bayesian models based on normal distributions or other conjugate structures typically resolve conflicts by centring the posterior at some compromise position, but this is not a realistic resolution when it means that the posterior is then in conflict with the different information sources. Bayesian modelling with heavy-tailed distributions has been shown to produce more reasonable conflict resolution, typically by favouring one source of information over the other. The less favoured source is ultimately wholly or partially rejected as the conflict becomes increasingly extreme.

The literature reviewed here provides formal proofs of conflict 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.”

Article information

Source
Braz. J. Probab. Stat., Volume 26, Number 4 (2012), 372-401.

Dates
First available in Project Euclid: 3 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1341320249

Digital Object Identifier
doi:10.1214/11-BJPS164

Mathematical Reviews number (MathSciNet)
MR2949085

Zentralblatt MATH identifier
1319.62064

Keywords
Built-in robustness heavy-tailed modelling outliers partial rejection of information rejection of information theory of conflict resolution

Citation

O’Hagan, Anthony; Pericchi, Luis. Bayesian heavy-tailed models and conflict resolution: A review. Braz. J. Probab. Stat. 26 (2012), no. 4, 372--401. doi:10.1214/11-BJPS164. https://projecteuclid.org/euclid.bjps/1341320249


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