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

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.

References in corpus (5)

• Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems
• The pseudo-marginal approach for efficient Monte Carlo computations
• Approximation and inference methods for stochastic biochemical kinetics - a tutorial review
• Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art
• The complex chemical Langevin equation

Cited by in corpus (5)

• Rapid Bayesian inference for expensive stochastic models
• Multifidelity multilevel Monte Carlo to accelerate approximate Bayesian parameter inference for partially observed stochastic processes
• Generalised likelihood profiles for models with intractable likelihoods
• Mathematical modelling and uncertainty quantification for analysis of biphasic coral reef recovery patterns
• Approximate solutions of a general stochastic velocity-jump model subject to discrete-time noisy observations