Improving predictive distributions

Abstract

Consider a sequence of decision problemsS 1,S 2, ... and suppose that in problemS i the statistician must specify his predictive distributionF i for some random variableX i and then make a decision based on that distribution. For example,X i might be the return on some particular investment and the statistician must decide whether or not to make that investment. The random variablesX 1,X 2 ... are assumed to be independent and completely unrelated. It is also assumed that each predictive distributionF i assigned by the statistician is a subjective distribution based on his information and beliefs aboutX i. In this context, the standard Bayesian approach provides no basis for evaluating whether the statistician's subjective predictive distribution forX i is good or bad, and does not even recognize this question as being meaningful. In this paper we describe models in which the statistician can study his process for specifying predictive distributions identify bad habits, and improve his predictions and decisions by gradually breaking these habits.