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.
Publié le : 1992-12-14
Classification:
Probability assessment methods,
probability elicitation,
prior distribution,
variable selection,
linear regression,
62F15,
62C10,
62J05
@article{1176348886,
author = {Garthwaite, Paul H. and Dickey, James M.},
title = {Elicitation of Prior Distributions for Variable-Selection Problems in Regression},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1697-1719},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348886}
}
Garthwaite, Paul H.; Dickey, James M. Elicitation of Prior Distributions for Variable-Selection Problems in Regression. Ann. Statist., Tome 20 (1992) no. 1, pp. 1697-1719. http://gdmltest.u-ga.fr/item/1176348886/