Abstract
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.
Highlights
When using quantitative models to explore biological or physical phenomena, it is crucial to be able to estimate parameters of these models and account appropriately for uncertainty in both the parameters and model predictions
We show by using standard arguments that the adaptive approximate Bayesian computation (ABC)-sequential Monte Carlo (SMC) algorithm given by Algorithm 2 will converge to the correct ABC posterior distribution
For some of these models it is possible to solve for the likelihood analytically, and we show comparisons with exact posterior distributions sampled via Markov Chain Monte Carlo (MCMC)
Summary
When using quantitative models to explore biological or physical phenomena, it is crucial to be able to estimate parameters of these models and account appropriately for uncertainty in both the parameters and model predictions. Much of the current theory surrounding the generation of posterior distributions for parameter inference relies on being able to evaluate the likelihood of the data given the parameters of a model. Pseudo-marginal MCMC and particle Markov Chain Monte Carlo (pMCMC) methods [12,13,14,15,16] provide exact inference for intractable distributions including state space models. PMCMC methods often have extremely low acceptance rates and poor mixing properties Methods to mitigate these issues include the use of noisy Monte Carlo methods [17, 18], but these no longer provide exact inference, and correlating the pseudorandom numbers used to estimate the likelihood [19]. The focus of this work, will be on one of the most popular methods for likelihood-free inference, approximate Bayesian computation (ABC) [20,21,22,23,24,25], which has been widely adopted due to its ease of understanding and implementation
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