Journal ArticleDOI
A note on bounded influence in Bayesian analysis
Luis R. Pericchi,Bruno Sansó +1 more
TLDR
In this article, the authors considered priors and likelihoods for the location problem which have bounded but nonvanishing influence on posterior moments and provided sufficient conditions for the posterior distribution of 0 to approach the prior distribution as x tends to infinity.Abstract:
SUMMARY Let x be a single observation from a distribution having unknown location parameter 0. Dawid (1973) provided sufficient conditions for the posterior distribution of 0 to approach the prior distribution as x tends to infinity, so that an outlier has bounded and vanishing influence on the posterior distribution. We present a result closely related to Dawid's theorem. This enables us to consider priors and likelihoods for the location problem which have bounded but nonvanishing influence on posterior moments. Examples are given.read more
Citations
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Journal ArticleDOI
Bayesian heavy-tailed models and conflict resolution: A review
Anthony O'Hagan,Luis R. Pericchi +1 more
TL;DR: It is shown that 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.
Journal ArticleDOI
Bayesian robustness modeling using regularly varying distributions
TL;DR: In this article, the authors use regular variation theory to establish sufficient conditions in the pure scale parameter structure under which it is possible to resolve conflicts among the sources of information. But the authors also note some important differences between the scale and the location parameters cases.
Journal ArticleDOI
Approximate Bayesian inference for random effects meta-analysis
Keith R. Abrams,Bruno Sansó +1 more
TL;DR: Simple approximations for the first and second moments of the parameters of a Bayesian random effects model for meta-analysis are considered and are shown to lead to sensible approximation in two examples of meta-analyses.
Journal ArticleDOI
Robust likelihood functions in Bayesian inference
TL;DR: In this paper, robust pseudo-likelihoods have been used to prevent the effects caused by model misspecifications, i.e. when the underlying distribution lies in a neighborhood of the assumed model.
Journal ArticleDOI
A case for robust Bayesian priors with applications to clinical trials
TL;DR: In this paper, the authors show how the robustness of conjugate Bayesian analysis can be improved by employing Cauchy priors with polynomial tails, such as Student's $t$.
References
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Journal ArticleDOI
On Outlier Rejection Phenomena in Bayes Inference
TL;DR: In this paper, it is shown that any admissible inference procedure applied to a t sample will effectively ignore extreme outlying observations regardless of prior information, while the normal distribution is outlier-resistant.
Journal ArticleDOI
Robust Bayesian credible intervals and prior ignorance
Luis Rauil Pericchi,Peter Walley +1 more
TL;DR: In this article, the authors survey and compare some classes of probability densities that may be used to represent partial prior information, to model either prior ignorance or Bayesian sensitivity analysis, and discuss various desiderata for a'reasonable' class, including coherence and sensible dependence of inferences on sample size.
Journal ArticleDOI
Posterior Cumulant Relationships in Bayesian Inference Involving the Exponential Family
TL;DR: For Bayesian inference in one-parameter contexts where either the likelihood or the prior has an exponential family form, relationships are derived for posterior moments and cumulants of (functions of) both the canonical and the expectation parameters as discussed by the authors.
Journal ArticleDOI
Near ignorance classes of log-concave priors for the location model
Bruno Sansó,Luis R. Pericchi +1 more
TL;DR: In this paper, the feasibility of near ignorance classes using log-concave distributions such as the logistic and the Box and Tiao exponential power family was studied. And the main conclusion was that exponential tails are the lightest permitted in order to produce NICs with non-vacuous posterior inference, for the normal location model.