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11
Diagnostic Measures for Model Criticism
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1996
"... ... 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 mo ..."
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... 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.
An efficient computational approach for prior sensitivity analysis and crossvalidation
 LA REVUE CANADIENNE DE STATISTIQUE
, 2010
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Robust Bayesian analysis using divergence measures under weighted distribution
, 1999
"... 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 considere ..."
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Cited by 5 (0 self)
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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 fflcontaminated 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...
On a Global Sensitivity Measure for Bayesian Inference
"... 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 a ..."
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Cited by 3 (0 self)
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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 ...
ASYMPTOTIC GLOBAL ROBUSTNESS IN BAYESIAN DECISION THEORY
, 2004
"... 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 ar ..."
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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
A Dirichlet Process Elaboration Diagnostic for Binomial Goodness of Fit
"... Useful model checking tools can be constructed by measuring the distance between a prior distribution that concentrates most of its mass around a model of interest and the resulting posterior distribution. In this paper we use this approach to construct a diagnostic measure for detecting lack of fit ..."
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Useful model checking tools can be constructed by measuring the distance between a prior distribution that concentrates most of its mass around a model of interest and the resulting posterior distribution. In this paper we use this approach to construct a diagnostic measure for detecting lack of fit in discrete data, with special focus on binomial data. We begin by constructing a suitable probability model "around" the model of interest, via a Dirichlet Process elaboration. We derive the resulting diagnostics and show that, approximately, it is the sum of two terms: the first is the logarithm of the Bayes factor and the second is proportional to the Pearson chisquare statistics. We give details of a simulation algorithm for computing the diagnostic and illustrate its use in an application to biomedical data. Keywords: Bayesian model criticism, binomial data, logarithmic divergence, chisquare statistics. Running Title: Binomial Goodness of Fit 1 Introduction Diagnostic measures are ...
Paper No. 0722w3, www.warwick.ac.uk/go/crism Isoseparation and Robustness in Finite Parameter Bayesian Inference
, 2008
"... Under a new family of separations the distance between two posterior densities is the same as the distance between their prior densities whatever the observed likelihood when that likelihood is strictly positive. Local versions of such separations form the basis of a weak topology having close lin ..."
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Under a new family of separations the distance between two posterior densities is the same as the distance between their prior densities whatever the observed likelihood when that likelihood is strictly positive. Local versions of such separations form the basis of a weak topology having close links to the Euclidean metric on the natural parameters of two exponential family densities. Using these local separation measures it is shown that when the tails of the approximating density have appropriate properties, the variation distance between an approximating posterior density to a genuine density can be bounded explicitly. These bounds apply irrespective of whether the prior densities are grossly misspecified with respect to variation distance and irrespective of the form or the validity of the observed likelihood.
sensitivity analysis and crossvalidation
"... La revue canadienne de statistique ..."
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Bayesian Inference Under Partial Prior Information
"... ABSTRACT. Partial prior information on the marginal distribution of an observable random variable is considered. When this information is incorporated into the statistical analysis of an assumed parametric model, the posterior inference is typically nonrobust so that no inferential conclusion is ob ..."
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ABSTRACT. Partial prior information on the marginal distribution of an observable random variable is considered. When this information is incorporated into the statistical analysis of an assumed parametric model, the posterior inference is typically nonrobust so that no inferential conclusion is obtained. To overcome this difficulty a method based on the standard default prior associated to the model and an intrinsic procedure is proposed. Posterior robustness of the resulting inferences is analysed and some illustrative examples are provided.
On the Brittleness of Bayesian Inference
, 2014
"... With the advent of highperformance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in increasingly complicated contexts, the sensitivity of their ..."
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With the advent of highperformance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in increasingly complicated contexts, the sensitivity of their posterior conclusions with respect to the underlying models and prior beliefs is a pressing question for which there currently exist positive and negative results. We report new results suggesting that, although Bayesian methods are robust when the number of possible outcomes is finite or when only a finite number of marginals of the datagenerating distribution are unknown, they are generically brittle when applied to continuous systems (and their discretizations) with finite information on the datagenerating distribution. If closeness is defined in terms of the total variation metric or the matching of a finite system of moments, then (1) two practitioners who use arbitrarily close models and observe the same (possibly arbitrarily large amount of) data may reach opposite conclusions; and (2) any given prior and model can be slightly perturbed to achieve