Likelihood free inference for Markov processes: a comparison

TL;DR

This paper compares likelihood-free inference methods, ABC and MCMC, for stochastic kinetic models in systems biology, analyzing their computational efficiency and effectiveness across different observation scenarios.

Contribution

It provides a comparative analysis of ABC and likelihood-free MCMC methods specifically for stochastic kinetic models, highlighting their relative strengths and weaknesses.

Findings

ABC and MCMC have different computational costs and efficiencies.

Observation regimes significantly affect inference quality.

Likelihood-free methods are viable for complex biological models.

Abstract

Approaches to Bayesian inference for problems with intractable likelihoods have become increasingly important in recent years. Approximate Bayesian computation (ABC) and "likelihood free" Markov chain Monte Carlo techniques are popular methods for tackling inference in these scenarios but such techniques are computationally expensive. In this paper we compare the two approaches to inference, with a particular focus on parameter inference for stochastic kinetic models, widely used in systems biology. Discrete time transition kernels for models of this type are intractable for all but the most trivial systems yet forward simulation is usually straightforward. We discuss the relative merits and drawbacks of each approach whilst considering the computational cost implications and efficiency of these techniques. In order to explore the properties of each approach we examine a range of observation regimes using two example models. We use a Lotka--Volterra predator prey model to explore the impact of full or partial species observations using various time course observations under the assumption of known and unknown measurement error. Further investigation into the impact of observation error is then made using a Schl\"ogl system, a test case which exhibits bi-modal state stability in some regions of parameter space.