Journal Article

An automatic adaptive method to combine summary statistics in approximate Bayesian computation

Harrison, Jonathan U., Baker, Ruth E.

2020

Overview

To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is that parameter inference must generally rely on summary statistics of the data. This is particularly the case for problems involving high-dimensional data, such as biological imaging experiments. However, some summary statistics contain more information about parameters of interest than others, and it is not always clear how to weight their contributions within the ABC framework. We address this problem by developing an automatic, adaptive algorithm that chooses weights for each summary statistic. Our algorithm aims to maximize the distance between the prior and the approximate posterior by automatically adapting the weights within the ABC distance function. Computationally, we use a nearest neighbour estimator of the distance between distributions. We justify the algorithm theoretically based on properties of the nearest neighbour distance estimator. To demonstrate the effectiveness of our algorithm, we apply it to a variety of test problems, including several stochastic models of biochemical reaction networks, and a spatial model of diffusion, and compare our results with existing algorithms.

• Publisher: Public Library of Science,Public Library of Science (PLoS)
• Subject: Adaptive algorithms / Algorithms / Automation / Bayes Theorem / Bayesian analysis / Biochemical Phenomena / Biometry - methods / Computation / Computational biology / Computer Simulation / Engineering and Technology / Funding / Likelihood Functions / Markov analysis / Markov Chains / Mathematical models / Metabolic Networks and Pathways / Methods / Models, Biological / Models, Statistical / Monte Carlo Method / Parameters / Physical Sciences / Regression Analysis / Research and Analysis Methods / Statistical analysis / Statistical inference / Statistics / Stochastic models / Stochastic Processes / Stochasticity