A practical guide to pseudo-marginal methods for computational inference in systems biology

TL;DR

This paper introduces pseudo-marginal methods for likelihood-free inference in systems biology, demonstrating their advantages over approximate Bayesian computation through case studies and Julia implementations.

Contribution

It provides a practical guide and case studies on applying pseudo-marginal methods for inference in biochemical reaction networks, highlighting their benefits over traditional methods.

Findings

Pseudo-marginal methods enable exact inference in complex stochastic models.

Combining pseudo-marginal methods with particle filters improves likelihood estimation accuracy.

Julia implementations facilitate practical application of these algorithms.

Abstract

For many stochastic models of interest in systems biology, such as those describing biochemical reaction networks, exact quantification of parameter uncertainty through statistical inference is intractable. Likelihood-free computational inference techniques enable parameter inference when the likelihood function for the model is intractable but the generation of many sample paths is feasible through stochastic simulation of the forward problem. The most common likelihood-free method in systems biology is approximate Bayesian computation that accepts parameters that result in low discrepancy between stochastic simulations and measured data. However, it can be difficult to assess how the accuracy of the resulting inferences are affected by the choice of acceptance threshold and discrepancy function. The pseudo-marginal approach is an alternative likelihood-free inference method that utilises a Monte Carlo estimate of the likelihood function. This approach has several advantages, particularly in the context of noisy, partially observed, time-course data typical in biochemical reaction network studies. Specifically, the pseudo-marginal approach facilitates exact inference and uncertainty quantification, and may be efficiently combined with particle filters for low variance, high-accuracy likelihood estimation. In this review, we provide a practical introduction to the pseudo-marginal approach using inference for biochemical reaction networks as a series of case studies. Implementations of key algorithms and examples are provided using the Julia programming language; a high performance, open source programming language for scientific computing.