  Parametric stochastic simulators are ubiquitous in science, often featuring
high-dimensional input parameters and/or an intractable likelihood. Performing
Bayesian parameter inference in this context can be challenging. We present a
neural simulation-based inference algorithm which simultaneously offers
simulation efficiency and fast empirical posterior testability, which is unique
among modern algorithms. Our approach is simulation efficient by simultaneously
estimating low-dimensional marginal posteriors instead of the joint posterior
and by proposing simulations targeted to an observation of interest via a prior
suitably truncated by an indicator function. Furthermore, by estimating a
locally amortized posterior our algorithm enables efficient empirical tests of
the robustness of the inference results. Since scientists cannot access the
ground truth, these tests are necessary for trusting inference in real-world
applications. We perform experiments on a marginalized version of the
simulation-based inference benchmark and two complex and narrow posteriors,
highlighting the simulator efficiency of our algorithm as well as the quality
of the estimated marginal posteriors.
