Finding a posterior domain probability distribution by specifying nonspecific evidence

This article is an extension of the results of two earlier articles. In (J. Schubert, "On nonspecific evidence", Int. J. Intell. Syst. 8(1993) 711-725) we established within Dempster-Shafer theory a criterion function called the metaconflict function. With this criterion we can partition into subsets a set of evidences with propositions that are weakly specified in the sense that it may be uncertain to which event a proposion is referring. In a second article (J. Schubert, "Specifying nonspecific evidence", FOA Report C20975-2.7, National Defence Research Establishment, Sundbyberg, 1994) we not only found the most plausible subset for each piece of evidence, we also found the plausibility for every subset that the evidence belongs to the subset. In this article we aim to find aposteri probability distribution regarding the number of subsets. We use the idea that each evidence in a subset supports the existence of that subset to the degree that the evidence supports anything at all. From this we can derive a bpa that is concerned with the question of how many subset we have. That bpa can then be combined with a given prior domain probability distribution in order to obtain the sought-after posterior domain distribution.