  We present simple methods for out-of-distribution detection using a trained
generative model. These techniques, based on classical statistical tests, are
model-agnostic in the sense that they can be applied to any differentiable
generative model. The idea is to combine a classical parametric test (Rao's
score test) with the recently introduced typicality test. These two test
statistics are both theoretically well-founded and exploit different sources of
information based on the likelihood for the typicality test and its gradient
for the score test. We show that combining them using Fisher's method overall
leads to a more accurate out-of-distribution test. We also discuss the benefits
of casting out-of-distribution detection as a statistical testing problem,
noting in particular that false positive rate control can be valuable for
practical out-of-distribution detection. Despite their simplicity and
generality, these methods can be competitive with model-specific
out-of-distribution detection algorithms without any assumptions on the
out-distribution.
