The Annals of Statistics

Robust Bayesian analysis of selection models

M. J. Bayarri and James Berger

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Selection models arise when the data are selected to enter the sample only if they occur in a certain region of the sample space. When this selection occurs according to some probability distribution, the resulting model is often instead called a weighted distribution model. In either case the "original" density becomes multiplied by a "weight function" $w(x)$. Often there is considerable uncertainty concerning this weight function; for instance, it may be known only that $w$ lies between two specified weight functions. We consider robust Bayesian analysis for this situation, finding the range of posterior quantities of interest, such as the posterior mean or posterior probability of a set, as $w$ ranges over the class of weight functions. The variational analysis utilizes concepts from variation diminishing transformations.

Article information

Ann. Statist. Volume 26, Number 2 (1998), 645-659.

First available in Project Euclid: 31 July 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G35: Robustness
Secondary: 62A15 62F15: Bayesian inference

Weighted distributions robust Bayes nonparametric classes of weight functions posterior bounds variation diminishing transformations


Bayarri, M. J.; Berger, James. Robust Bayesian analysis of selection models. Ann. Statist. 26 (1998), no. 2, 645--659. doi:10.1214/aos/1028144852.

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