  Bayesian inference for complex models with an intractable likelihood can be
tackled using algorithms performing many calls to computer simulators. These
approaches are collectively known as "simulation-based inference" (SBI). Recent
SBI methods have made use of neural networks (NN) to provide approximate, yet
expressive constructs for the unavailable likelihood function and the posterior
distribution. However, the trade-off between accuracy and computational demand
leaves much space for improvement. In this work, we propose an alternative that
provides both approximations to the likelihood and the posterior distribution,
using structured mixtures of probability distributions. Our approach produces
accurate posterior inference when compared to state-of-the-art NN-based SBI
methods, even for multimodal posteriors, while exhibiting a much smaller
computational footprint. We illustrate our results on several benchmark models
from the SBI literature and on a biological model of the translation kinetics
after mRNA transfection.
