Aggregazioni di Probabilità

We develop a new outlook on the use of experts' probabilities for inference, distinguishing the information content available to them from their probability assertions based on that information. It allows a statistician to specify a flexible function that represents a posterior probability of interest conditioned on all the information available to any of the experts. We work here in the restricted case of one expert, but the results are extendible in a variety of ways. The combining function is computed from statistics provided by the expert personal probability assertions which are based on the data. Considered as functions of the data through the individual expert assessing functions, they thus provide a statistic. Given some assumptions this assertion is shown to be sufficient for the direct computation of thedesired posterior probability. We develop a mixture distribution structure that allows integration in one dimension to yield the complete computation.