  We formulate and analyze a stochastic threshold group testing problem
motivated by biological applications. Here a set of $n$ items contains a subset
of $d \ll n$ defective items. Subsets (pools) of the $n$ items are tested --
the test outcomes are negative, positive, or stochastic (negative or positive
with certain probabilities that might depend on the number of defectives being
tested in the pool), depending on whether the number of defective items in the
pool being tested are fewer than the {\it lower threshold} $l$, greater than
the {\it upper threshold} $u$, or in between. The goal of a {\it stochastic
threshold group testing} scheme is to identify the set of $d$ defective items
via a "small" number of such tests. In the regime that $l = o(d)$ we present
schemes that are computationally feasible to design and implement, and require
near-optimal number of tests (significantly improving on existing schemes). Our
schemes are robust to a variety of models for probabilistic threshold group
testing.
