Efficient Bayesian Inference for Nested Simulators

Abstract

We introduce two approaches for conducting efficient Bayesian inference in stochastic simulators containing nested stochastic sub-procedures, i.e., internal procedures such as rejection sampling loops for which the density cannot calculated directly. Such simulators are standard through the sciences and can be interpreted as probabilistic generative models. However, drawing inferences from them poses a substantial challenge due to the inability to evaluate even their unnormalised density. To address this, we introduce inference algorithms based on a two-step procedure where one first tackle the sub-procedures as amortised inference problems then uses the learned artefacts to construct an approximation of the original unnormalised density that can be used as a target for Markov chain Monte Carlo methods. Because the sub-procedures can be dealt with separately and are lower-dimensional than that of the overall problem, this two-step process allows them to be isolated and thus be tractably dealt with, without placing restrictions on the overall dimensionality of the problem. We demonstrate the utility of our methods on a simple, artificially constructed simulator.