... In this article we present the general outlook and discuss general families of elaborations for use in practice; the exponential connection elaboration plays a key role. We then describe model elaborations for use in diagnosing: departures from normality, goodness of fit in generalized linear models, and variable selection in regression and outlier detection. We illustrate our approach with two applications.

This paper considers the use of the limiting local '-divergence measures between posterior weighted distribtions and two weighted distributions under classes of contaminated weighted functions. Two classes of weighted functions in the neighborhood of the elicited weighted function are considered, one is the usual ffl-contaminated class and the other one is a geometric mixing class. A global measure, using the limiting local '-divergence between two posterior weighted distributions and two weighted distributions, is introduced. Calculation of ranges of the limiting local '-divergence is demonstrated through examples. It is shown that the limiting local '-divergence formulas give unified answers irrespective of the choice of '-functions. Key words and Phrases: Local sensitivity, Bayesian robustness, Perturbation, '- divergence, Posterior weighted distribution, Weighted distribution. AMS 1990 subject classification: 62A15, 62F15 1.Introduction There are many situations where the usual...

We define a global sensitivity measure that is useful in assessing sensitivity to deviations from a specified prior. We argue that this measure has a common interpretation irrespective of the context of the problem, or the unit of measurements, and is therefore easy to interpret. We also study the asymptotic behavior of this global sensitivity measure. We find that it does not always converge to 0 as the sample size goes to infinity. We also show that, under certain conditions, this measure does go to 0 as the sample size goes to infinity. Thus, unlike the usual global sensitivity measure range, this measure behaves asymptotically like the usual local sensitivity measure. 1 AMS 1991 subject classifications. Primary 62F35; secondary 62C10 Key words and phrases. Bayesian robustness, global sensitivity, asymptotics. 1 1 Introduction In a Bayesian analysis involving a subjectively elicited prior, one is usually concerned with sensitivity to deviations from the specified prior, 0 . In ...

Abstract not found

In Bayesian decision theory, it is known that robustness with respect to the loss and the prior can be improved by adding new observations. In this article we study the rate of robustness improvement with respect to the number of observations n. Three usual measures of posterior global robustness are considered: the (range of the) Bayes actions set derived from a class of loss functions, the maximum regret of using a particular loss when the subjective loss belongs to a given class and the range of the posterior expected loss when the loss function ranges over a class. We show that the rate of convergence of the first measure of robustness is √ n, while it is n for the other measures under reasonable assumptions on the class of loss functions. We begin with the study of two particular cases to illustrate our results. 1. Introduction. In Bayesian analysis