  Many recent works in simulation-based inference (SBI) rely on deep generative
models to approximate complex, high-dimensional posterior distributions.
However, evaluating whether or not these approximations can be trusted remains
a challenge. Most approaches evaluate the posterior estimator only in
expectation over the observation space. This limits their interpretability and
is not sufficient to identify for which observations the approximation can be
trusted or should be improved. Building upon the well-known classifier
two-sample test (C2ST), we introduce L-C2ST, a new method that allows for a
local evaluation of the posterior estimator at any given observation. It offers
theoretically grounded and easy to interpret -- e.g. graphical -- diagnostics,
and unlike C2ST, does not require access to samples from the true posterior. In
the case of normalizing flow-based posterior estimators, L-C2ST can be
specialized to offer better statistical power, while being computationally more
efficient. On standard SBI benchmarks, L-C2ST provides comparable results to
C2ST and outperforms alternative local approaches such as coverage tests based
on highest predictive density (HPD). We further highlight the importance of
local evaluation and the benefit of interpretability of L-C2ST on a challenging
application from computational neuroscience.
