MATHEMATICAL MODELS FOR ELICITATION IN BAYESIAN REGRESSION

THIS RESEARCH PROGRAM WILL DEVELOP AND EXTEND THE MATHEMATICAL THEORY UNDERLYING THE ELICITATION OF PROBABILITY DISTRIBUTIONS FOR USE IN BAYESIAN REGRESSION ANALYSES. INCORPORATING EXPERT OPINION IN THE FORM OF PROBABILITY DISTRIBUTIONS IS ESSENTIAL IN APPLICATIONS FOR WHICH AVAILABLE DATA ARE INSUFFICIENT FOR OBTAINING PRECISE PARAMETER ESTIMATES USING CLASSICAL ESTIMATION TECHNIQUES, BUT FOR WHICH SUBSTANTIAL INFORMATION IS AVAILABLE IN THE FORM OF EXPERT KNOWLEDGE. EARLIER WORK BY THE PROJECT TEAM HAS RESULTED IN GENERALLY APPLICABLE ELICITATION METHODOLOGYFOR STANDARD REGRESSION MODELS. THE GOAL OF PHASE I RESEARCH IS TO DEVELOP THEORY FOR ELICITING NEW TYPES OF MODELS FROM AN EXPERT'S JUDGMENT ABOUT FUTURE HYPOTHETICAL OBSERVATION; AND TO ESTABLISH THE FEASIBILITY OF FURTHER THEORETICAL ADVANCES AND SOFTWARE DEVELOPMENT DURING PHASE II. FOUR RESEARCH OBJECTIVES FOR PHASE I HAVE BEEN IDENTIFIED:(1)INVESTIGATE THE RELAXATION OF ASSUMPTIONS UNDERLYING EXISTING ELICITATION MODELS--ESPECIALLY EXTENDINGTHE METHODS TO MODELS FOR DETECTING OUTLIERS;(2)DEVELOP THEORY TO EXPLOIT THE STRUCTURE OF SPECIAL CASES OF THE NORMAL LINEAR MODEL (SUCH AS HIERARCHICAL PRIORS FOR ANOVA MODELS);(3)DEVELOP METHODS FOR ELICITING PRIOR INFORMATION ABOUT COMMON STATISTICAL MODELS OTHER THAN THE NORMAL LINEAR MODEL; AND (4) DEVELOP IMPROVED COMPUTATIONAL TECHNIQUES WHEN EXPERT JUDGMENTS DO NOT LEAD TO CLOSED-FORM SOLUTIONS FOR PRIOR PARAMETERS.