  In this paper, an exact bitwise MAP (Maximum A Posteriori) estimation
algorithm for group testing problems is presented. We assume a simplest
non-adaptive group testing scenario including N-objects with binary status and
M-disjunctive tests. If a group contains a positive object, the test result for
the group is assumed to be one; otherwise, the test result becomes zero. Our
inference problem is to evaluate the posterior probabilities of the objects
from the observation of M-test results and from our knowledge on the prior
probabilities for objects. The heart of the algorithm is the dual expression of
the posterior values. The derivation of the dual expression can be naturally
described based on a holographic transformation to the normal factor graph
(NFG) representing the inference problem.
