ELICITATION OF PRIOR DISTRIBUTIONS FOR VARIABLE-SELECTION PROBLEMS IN REGRESSION

• 成果类型: Article
• 署名作者: GARTHWAITE, PH; DICKEY, JM
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348886
• 发表日期: 1992
• 页码: 1697-1719
• 关键词: design; models

摘要

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.