  We describe a novel way to represent the probability distribution of a random
binary string as a mixture having a maximally weighted component associated
with independent (though not necessarily identically distributed) Bernoulli
characters. We refer to this as the latent independent weight of the
probabilistic source producing the string, and derive a combinatorial algorithm
to compute it. The decomposition we propose may serve as an alternative to the
Boolean paradigm of hypothesis testing, or to assess the fraction of
uncorrupted samples originating from a source with independent marginals. In
this sense, the latent independent weight quantifies the maximal amount of
independence contained within a probabilistic source, which, properly speaking,
may not have independent marginals.
