## The Annals of Statistics

### Robust Bayesian analysis of selection models

#### Abstract

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

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

Dates
First available in Project Euclid: 31 July 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1028144852

Digital Object Identifier
doi:10.1214/aos/1028144852

Mathematical Reviews number (MathSciNet)
MR1626067

Zentralblatt MATH identifier
0929.62058

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

#### Citation

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

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• DURHAM, NORTH CAROLINA 27708-0251
• 46100 BURJASSOT, VALENCIA E-MAIL: berger@stat.duke.edu SPAIN E-MAIL: bay arri@uv.es