  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 several pieces of evidence with propositions that are weakly specified in
the sense that it may be uncertain to which event a proposition is referring.
In a second article [J. Schubert, Specifying nonspecific evidence, in
Cluster-based specification techniques in Dempster-Shafer theory for an
evidential intelligence analysis of multiple target tracks, Ph.D. Thesis,
TRITA-NA-9410, Royal Institute of Technology, Stockholm, 1994, ISBN
91-7170-801-4] we not only found the most plausible subset for each piece of
evidence, we also found the plausibility for every subset that this piece of
evidence belongs to the subset. In this article we aim to find a posterior
probability distribution regarding the number of subsets. We use the idea that
each piece of evidence in a subset supports the existence of that subset to the
degree that this piece of evidence supports anything at all. From this we can
derive a bpa that is concerned with the question of how many subsets 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.
