Improving predictive distributions

Consider a sequence of decision problems S1, S2, ... and suppose that in problem Si the statistician must specify his predictive distribution Fi for some random variable Xi and make a decision based on that distribution. For example, Xi might be the return on some particular investment and the statistician must decide whether or not to make that investment. The random variables X1, X2, ... are assumed to be independent and completely unrelated. It is also assumed that each predictive distribution Fi assigned by the statistician is a subjective distribution based on his information and beliefs about Xi. In this context, the standard Bayesian approach provides no basis for evaluating whether the statistician's subjective predictive distribution for Xi 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