A practical guide to pseudo-marginal methods for computational inference in systems biology. (7th July 2020) - Warne, David J.; Baker, Ruth E.; Simpson, Matthew J.
Highlights: Stochastic models of biochemical processes almost always lead to intractable inference problems. The popular likelihood-free method, approximate Bayesian computation (ABC), is compared and contrasted with pseudo-marginal methods that have significant accuracy advantages over ABC. The review is designed to be accessible to researchers without a strong computational statistics background. All ideas are presented through practical examples, including stochastic models of gene regulatory networks. Example open source code, using the Julia programminng language, are provided for all examples included in the review. 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 (https://github.com/davidwarne/Warne2019_GuideToPseudoMarginal ).