## The Annals of Statistics

### Elicitation of Prior Distributions for Variable-Selection Problems in Regression

#### Abstract

This paper addresses the problem of quantifying expert opinion about a normal linear regression model when there is uncertainty as to which independent variables should be included in the model. Opinion is modeled as a mixture of natural conjugate prior distributions with each distribution in the mixture corresponding to a different subset of the independent variables. It is shown that for certain values of the independent variables, the predictive distribution of the dependent variable simplifies from a mixture of $t$-distributions to a single $t$-distribution. Using this result, a method of eliciting the conjugate distributions of the mixture is developed. The method is illustrated in an example.

#### Article information

Source
Ann. Statist. Volume 20, Number 4 (1992), 1697-1719.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348886

Digital Object Identifier
doi:10.1214/aos/1176348886

Mathematical Reviews number (MathSciNet)
MR1193309

Zentralblatt MATH identifier
0786.62043

JSTOR