Quantifying and using expert opinion for variable-selection problems in regression

This paper gives a general method for use in the chemical industry for eliciting and quantifying an expertʹs subjective opinion concerning a normal linear regression model. The intention is to ask the expert assessment questions that he or she can meaningfully answer and to use the elicited values to determine a probability distribution on the regression parameters that quantifies and expresses the expertʹs opinions. A regression model may represent a chemical production process, for example, and the corresponding elicited distribution would embody the expertʹs opinion concerning the effects on product output of independent variables for process control and environmental factors. It may be uncertain what independent variables should be featured in the regression, so the expertʹs opinion is represented by a mixture of multivariate distributions, where each distribution in the mixture corresponds to a different subset of independent variables. Among the uses to which an elicited distribution might be put is design of experiments, discussed here with regard to Bayesian design criteria. An example is given of the elicitation and use of a subjective distribution in which an industrial chemist quantified his opinion about a chemical process.