Master thesis : Conservative Simulation-Based Inference with Bayesian Deep Learning

Abstract

Simulation-Based Inference (SBI) involves estimating parameters θ of a simulator that are compatible with the observations x without evaluating the likelihood of the data. Currently, the best solutions for SBI are neural SBI methods, which are trained using datasets built with simulations. However, simulations can be computationally expensive in fields like meteorology or cosmology. Consequently, SBI methods can operate in a data-poor regime in these fields. When only a limited number of simulations are available, traditional SBI methods tend to be overconfident due to neural methods overfitting the data. This overfitting leads to computational uncertainty, as many neural networks may fit the training data equally well but perform differently on the test data. This thesis introduces a method using Bayesian Deep Learning (BDL) to account for computational uncertainty in SBI. We design a family of Bayesian Neural Network (BNN) priors that yield conservative results with as few as 10 samples, setting it apart from all other SBI methods. We demonstrate that the use of BDL in SBI produces informative and conservative posterior distribution estimates with only a few hundred simulations on a cosmological application. This advancement allows for drawing reliable scientific conclusions using our method, even when the number of available simulations is limited.