Multi-level Approximate Bayesian Computation

Approximate Bayesian Computation is widely used to infer the parameters of
discrete-state continuous-time Markov networks. In this work, we focus on
models that are governed by the Chemical Master Equation (the CME). Whilst
originally designed to model biochemical reactions, CME-based models are now
frequently used to describe a wide range of biological phenomena
mathematically. We describe and implement an efficient multi-level ABC method
for investigating model parameters. In short, we generate sample paths of
CME-based models with varying time resolutions. We start by generating
low-resolution sample paths, which require only limited computational resources
to construct. Those sample paths that compare well with experimental data are
selected, and the temporal resolutions of the chosen sample paths are
recursively increased. Those sample paths unlikely to aid in parameter
inference are discarded at an early stage, leading to an optimal use of
computational resources. The efficacy of the multi-level ABC is demonstrated
through two case studies.