  Hypothesis testing in high dimensional data is a notoriously difficult
problem without direct access to competing models' likelihood functions. This
paper argues that statistical divergences can be used to quantify the
difference between the population distributions of observed data and competing
models, justifying their use as the basis of a hypothesis test. We go on to
point out how modern techniques for functional optimization let us estimate
many divergences, without the need for population likelihood functions, using
samples from two distributions alone. We use a physics-based example to show
how the proposed two-sample test can be implemented in practice, and discuss
the necessary steps required to mature the ideas presented into an experimental
framework. The code used has been made available for others to use.
