Neural Posterior Estimation

Neural posterior estimation trains a model to map data to a distribution over the parameters that could have generated it, making Bayesian inference possible when a simulator exists but its likelihood is difficult to compute. Common approaches use normalizing flows, autoregressive models, diffusion or score-based methods, and learned summaries; some compress parameters or data, split large datasets into shards, or combine neural proposals with conventional samplers. These methods are tested on simulation-based inference benchmarks and in settings such as imaging, epidemiology, dynamical systems, and cognitive models, where they can turn repeated inference into fast posterior sampling. A central challenge is ensuring calibration and useful joint uncertainty when simulations are limited or differ from real data, since accurate parameter marginals do not always guarantee accurate predictions or dependencies.