Bayesian Abstraction of Markov Population Models

Abstract

Markov Population Models are a widespread formalism, with applications in Systems Biology, Performance Evaluation, Ecology, and many other fields. The associated Markov stochastic process in continuous time is often analyzed by simulation, which can be costly for large or stiff systems, particularly when simulations have to be performed in a multi-scale model (e.g. simulating individual cells in a tissue). A strategy to reduce computational load is to abstract the population model, replacing it with a simpler stochastic model, faster to simulate. Here we pursue this idea, building on previous work [3] and constructing an approximate kernel for a Markov process in continuous space and discrete time, capturing the evolution at fixed \(\varDelta t\) time steps. This kernel is learned automatically from simulations of the original model. Differently from [3], which relies on deep neural networks, we explore here a Bayesian density regression approach based on Dirichlet processes, which provides a principled way to estimate uncertainty.