Decision analysis: Perspectives on inference, decision, and experimentation

This paper illustrates by using a simple coin-tossing example how the new discipline of decision analysis sheds light on the perennial problems of inference, decision, and experimentation. The inference problem is first discussed from the classical viewpoints of maximum likelihood estimation and hypothesis testing, and then from the viewpoint of subjective probability and Bayesian updating. The problem is next placed in a decision setting to demonstrate how an estimate is related to the nature of the loss structure. Experimental possibilities are evaluated for the case where the size of the experiment must be determined a priori and for the case where experimentation can cease at any point. The decision-analysis philosophy allows consideration of all these problems within one philosophical and methodological framework.