  Our previous work on classifying complex ship images [1,2] has evolved into
an effort to develop software tools for building and solving generic
classification problems. Managing the uncertainty associated with feature data
and other evidence is an important issue in this endeavor. Bayesian techniques
for managing uncertainty [7,12,13] have proven to be useful for managing
several of the belief maintenance requirements of classification problem
solving. One such requirement is the need to give qualitative explanations of
what is believed. Pearl [11] addresses this need by computing what he calls a
belief commitment-the most probable instantiation of all hypothesis variables
given the evidence available. Before belief commitments can be computed, the
straightforward implementation of Pearl's procedure involves finding an
analytical solution to some often difficult optimization problems. We describe
an efficient implementation of this procedure using tensor products that solves
these problems enumeratively and avoids the need for case by case analysis. The
procedure is thereby made more practical to use in the general case.
