Bayesian Inverse Decision Theory

• Activity Number: 263
• Type: Topic Contributed
• Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Dennis D. Cox*+ and Kalatu Davies and Scott B. Cantor and Richard Swartz
• Companies: Rice University and Rice University and University of Texas M.D. Anderson Cancer Center and University of Texas M.D. Anderson Cancer Center
• Keywords: Bayesian sequential methods ; Bayesian inference ; medical decision-making ; cost-benefit analysis ; inverse decision theory

Abstract

Inverse decision theory concerns inferences about losses given a presumed optimal decision rule. In most settings, this provides only linear constraints on the losses. We consider settings where we have prior knowledge about the losses which is captured by a prior distribution on the losses. We show how this can be combined with the constraints from an inverse decision theoretic analysis to obtain a posterior on losses. Generalizations include (a) sequential procedures, where one also considers costs associated with data collection, and (b) uncertainty about the probabilistic model for the decision problem, which is also treated from a Bayesian perspective to obtain a unified approach to the overall problem. An application is given to the current standard of care for detecting precancerous lesions of the uterine cervix.