BayesFlow: Learning Complex Stochastic Models With Invertible Neural Networks

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit likelihood function is not available. With this work, we propose a novel method for globally amortized Bayesian inference based on invertible neural networks that we call BayesFlow. The method uses simulations to learn a global estimator for the probabilistic mapping from observed data to underlying model parameters. A neural network pretrained in this way can then, without additional training or optimization, infer full posteriors on arbitrarily many real data sets involving the same model family. In addition, our method incorporates a summary network trained to embed the observed data into maximally informative summary statistics. Learning summary statistics from data makes the method applicable to modeling scenarios where standard inference techniques with handcrafted summary statistics fail. We demonstrate the utility of BayesFlow on challenging intractable models from population dynamics, epidemiology, cognitive science, and ecology. We argue that BayesFlow provides a general framework for building amortized Bayesian parameter estimation machines for any forward model from which data can be simulated.

Automated summary

This article proposes a globally amortized Bayesian inference method called BayesFlow, based on invertible neural networks. The method learns a global estimator for the probabilistic mapping from observed data to model parameters using simulations. It can infer full posteriors on multiple real data sets without additional training, and incorporates a summary network to embed observed data into informative summary statistics. The utility of BayesFlow is demonstrated on intractable models from various fields.