Efficient Exact Inference for Dynamical Systems with Noisy Measurements using Sequential Approximate Bayesian Computation

Abstract

MotivationApproximate Bayesian Computation (ABC) is an increasingly popular method for likelihood-free parameter inference in systems biology and other fields of research, since it allows analysing complex stochastic models. However, the introduced approximation error is often not clear. It has been shown that ABC actually gives exact inference under the implicit assumption of a measurement noise model. Noise being common in biological systems, it is intriguing to exploit this insight. But this is difficult in practice, since ABC is in general highly computationally demanding. Thus, the question we want to answer here is how to efficiently account for measurement noise in ABC. ResultsWe illustrate exemplarily how ABC yields erroneous parameter estimates when neglecting measurement noise. Then, we discuss practical ways of correctly including the measurement noise in the analysis. We present an efficient adaptive sequential importance sampling based algorithm applicable to various model types and noise models. We test and compare it on several models, including ordinary and stochastic differential equations, Markov jump processes, and stochastically interacting agents, and noise models including normal, Laplace, and Poisson noise. We conclude that the proposed algorithm could improve the accuracy of parameter estimates for a broad spectrum of applications. AvailabilityThe developed algorithms are made publicly available as part of the open-source python toolbox pyABC (https://github.com/icb-dcm/pyabc). Contactjan.hasenauer@uni-bonn.de Supplementary informationSupplementary information is available at bioRxiv online. Supplementary code and data are available online at http://doi.org/10.5281/zenodo.3631120.