Bayesian robustness modeling using regularly varying distributions

By J. Andrade, Anthony OʼHagan. 2006

56 citations recorded by the source corpus.

Bayesian robustness modelling using heavy-tailed distributions provides a flexible approach to resolving problems of conflicts between the data and prior distributions. See Dawid (1973) and O’Hagan (1979, 1988, 1990), who provided sufficient conditions on the distributions in the model in order to reject the conflicting data or the prior distribution in favour of the other source of information. However, the literature has almost concentrated exclusively on robustness of the posterior distribution of location parameters; little attention has been given to scale parameters. In this paper we propose a new approach for Bayesian robustness modelling, in which we use the class of regularly varying distributions. Regular variation provides a very natural description of tail thickness in heavy-tailed distributions. Using regular variation theory, we establish sufficient conditions in the pure scale parameter structure under which is possible to resolve conflicts amongst the sources of information. We also note some important differences between the scale and the location parameters cases. Finally, we obtain new conditions in the pure location parameter structure which may be easier to verify than those proposed by Dawid and O’Hagan.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9d9bcc3b6b464f33c31c34728e9cf40297a1e06b

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In Statistics and Probability

Citations in the corpus

Bayesian heavy-tailed models and conflict resolution: A review (2012, methodology): “In particular, if g also has regularly varying right tail with RV-credence c′, then condition (F) simply requires c′ > c. Andrade and O’Hagan (2006) prove that then the limiting posterior density of θ is θc−1g(θ)∫ ∞ 0 θ c−1g(θ) dθ .”
Diagnostics of prior-data agreement in applied Bayesian analysis (2008, background): “Bousquet and Celeux [17] proposed to modify the posterior priors into pseudoposterior priors using the fractional likelihoods defined by O’Hagan [46,47].”