Improving predictive distributions

Summary

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.