  Modern simulation-based inference techniques use neural networks to solve
inverse problems efficiently. One notable strategy is neural posterior
estimation (NPE), wherein a neural network parameterizes a distribution to
approximate the posterior. This approach is particularly advantageous for
tackling low-latency or high-volume inverse problems. However, the accuracy of
NPE varies significantly within the learned parameter space. This variability
is observed even in seemingly straightforward systems like coupled-harmonic
oscillators. This paper emphasizes the critical role of prior selection in
ensuring the consistency of NPE outcomes. Our findings indicate a clear
relationship between NPE performance across the parameter space and the number
of similar samples trained on by the model. Thus, the prior should match the
sample diversity across the parameter space to promote strong, uniform
performance. Furthermore, we introduce a novel procedure, in which amortized
and sequential NPE are combined to swiftly refine NPE predictions for
individual events. This method substantially improves sample efficiency, on
average from nearly 0% to 10-80% within ten minutes. Notably, our research
demonstrates its real-world applicability by achieving a significant milestone:
accurate and swift inference of posterior distributions for low-mass binary
black hole (BBH) events with NPE.
