Behavioral Mapping of Hierarchical Dynamical Models Accelerates Bayesian Parameter Inference

Abstract

Bayesian parameter inference for complex nonlinear dynamical models is often limited by the cost of repeated model simulation. We present a behavioral mapping framework that uses the inferred posterior of a higher-level model to accelerate inference of a lower-level model without requiring state or parameter correspondence between them. Building on approximate simulation relations for hierarchically related models, we define the notion of behavioral compatibility and quantify the behavioral support of detailed model parameters using the reduced model posterior. We learn a level set of behavioral support using a Gaussian process and use it to filter detailed model parameter proposals before expensive simulations during Markov Chain Monte Carlo (MCMC) inference. We derive conditions under which the behavioral support level set retains all detailed model parameters that fit the experimental data within a prescribed tolerance. We apply this method to a hierarchy of gene-expression models fitted to cell-free experimental data. After initial setup costs, our approach speeds up MCMC by 8.02% for the phenomenological model and 15.21% for the mechanistic model.