Simultaneous identification of models and parameters of scientific
  simulators
Cornelius Schröder Jakob H. Macke
Many scientific models are composed of multiple discrete components, and
scien tists 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 an amortized simulation-based inference framework: We
define implicit model priors over a fixed set of candidate components and train
neural networks to infer joint probability distributions over both, model
components and associated parameters from simulations. To represent
distributions over model components, we introduce a conditional mixture of
multivariate binary distributions in the Grassmann formalism. Our approach can
be applied to any compositional stochastic simulator without requiring access
to likelihood evaluations. We first illustrate our method on a simple time
series model with redundant components and show that it can retrieve joint
posterior distribution over a set of symbolic expressions and their parameters
while accurately capturing redundancy with strongly correlated posteriors. We
then apply our approach to drift-diffusion models, a commonly used model class
in cognitive neuroscience. After validating the method on synthetic data, we
show that our approach explains experimental data as well as previous methods,
but that our fully probabilistic approach can help to discover multiple
data-consistent model configurations, as well as reveal non-identifiable model
components and parameters. Our method provides a powerful tool for data-driven
scientific inquiry which will allow scientists to systematically identify
essential model components and make uncertainty-informed modelling decisions.