Elicitation of prior distributions of variable-selection problems in regression

Garthwaite, Paul H. and Dickey, James M. (1992). Elicitation of prior distributions of variable-selection problems in regression. Annals of Statistics, 20(4) pp. 1697–1719.

DOI: https://doi.org/10.1214/aos/1176348886

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 -distributions to a single -distribution. Using this result, a method of eliciting the conjugate distributions of the mixture is developed. The method is illustrated in an example.

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