  Many scientific models are composed of multiple discrete components, and
scientists often make heuristic decisions about which components to include.
Bayesian inference provides a mathematical framework for systematically
selecting model components, but defining prior distributions over model
components and developing associated inference schemes has been challenging. We
approach this problem in a simulation-based inference framework: We define
model priors over candidate components and, from model simulations, train
neural networks to infer joint probability distributions over both model
components and associated parameters. Our method, simulation-based model
inference (SBMI), represents distributions over model components as a
conditional mixture of multivariate binary distributions in the Grassmann
formalism. SBMI can be applied to any compositional stochastic simulator
without requiring likelihood evaluations. We evaluate SBMI on a simple time
series model and on two scientific models from neuroscience, and show that it
can discover multiple data-consistent model configurations, and that it reveals
non-identifiable model components and parameters. SBMI provides a powerful tool
for data-driven scientific inquiry which will allow scientists to identify
essential model components and make uncertainty-informed modelling decisions.
