  Estimating prevalence, the fraction of a population with a certain medical
condition, is fundamental to epidemiology. Traditional methods rely on
classification of test samples taken at random from a population. Such
approaches to estimating prevalence are biased and have uncontrolled
uncertainty. Here, we construct a new, unbiased, minimum variance estimator for
prevalence. Recent result show that prevalence can be estimated from counting
arguments that compare the fraction of samples in an arbitrary subset of the
measurement space to what is expected from conditional probability models of
the diagnostic test. The variance of this estimator depends on both the choice
of subset and the fraction of samples falling in it. We employ a bathtub
principle to recast variance minimization as a one-dimensional optimization
problem. Using symmetry properties, we show that the resulting objective
function is well-behaved and can be numerically minimized.
