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

Abstract

Motivation: Approximate 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. Results:We 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, 1 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.Availability: The developed algorithms are made publicly available as part of the opensource python toolbox pyABC (https://github.com/icb-dcm/pyabc).

Anin vitro- agent-based modelling approach to optimisation of culture medium for generating muscle cells

“…The parameters γ, t MT fuse , k lat and k nuc form function subset L 2 ( α, β ). These parameters were derived via statistical inference using an approximate Bayesian computation sequential Monte Carlo (ABC-SMC) method[23]. ABC approximates a posterior distribution for each parameter by comparing the distance between summary statistics provided by the ABM with those measured from experimental images using a distance function ( δ ( x )).…”