PROJECT TITLE :

BayesFlow Learning Complex Stochastic Models With Invertible Neural Networks

ABSTRACT:

Estimating the parameters of mathematical models is a problem that arises frequently in virtually all subfields of the scientific discipline. On the other hand, when processes and model descriptions become increasingly complex and there is no explicit likelihood function available, this problem can become exceptionally challenging to solve. BayesFlow is the name we have given to our novel approach to globally amortized Bayesian inference that is based on invertible neural networks. This method was developed as part of this research. The method involves running simulations in order to learn a global estimator for the probabilistic mapping from observed data to the model parameters that lie beneath the surface. Inferring full posteriors on an arbitrary number of real data sets involving the same model family is something a neural network that has been pretrained in this manner is able to do without any additional training or optimization. In addition, our approach makes use of a summary network that is trained to embed the data that has been observed into summary statistics that are as informative as possible. The ability to learn summary statistics from data makes the method applicable to modeling scenarios in which standard inference techniques involving hand-crafted summary statistics fail. We demonstrate the usefulness of BayesFlow by applying it to difficult intractable models originating in population dynamics, epidemiology, cognitive science, and ecology. We contend that BayesFlow provides a general framework for building amortized Bayesian parameter estimation machines for any forward model from which data can be simulated. This is what we mean when we say that BayesFlow is a general framework.