Demonstrating the Power and Flexibility of Variational Assumptions for Amortized Neural Posterior Estimation in Environmental Applications

ABSTRACT Classic Bayesian methods with complex environmental models are frequently infeasible due to an intractable likelihood. Simulation‐based inference methods, such as neural posterior estimation, calculate posteriors without accessing a likelihood function by leveraging the fact that data can be quickly simulated from the model, but converge slowly and/or poorly in high‐dimensional settings. In this paper, we suggest that imposing strict variational assumptions on the form of the posterior can often combat these computational issues. Posterior distributions of model parameters are efficiently obtained by assuming a parametric form for the posterior, parametrized by the machine learning model, which is trained with the simulated data as inputs and the associated parameters as outputs. We show theoretically that if the parametric family of the variational posterior is correct, our posteriors converge to the true posteriors in Kullback–Leibler divergence. We also provide tools to help us identify if our parametric assumption is close to the true posterior, and modeling options if that is not the case. Comprehensive simulation studies using environmental models highlight our method's robustness and versatility. An analysis of the Zika virus in Brazil provides a thorough case study.