Selecting Summary Statistics in Approximate Bayesian Computation for Calibrating Stochastic Models

Approximate Bayesian computation (ABC) is an approach for using measurement data to calibrate stochastic computer models, which are common in biology applications. ABC is becoming the "go-to" option when the data and/or parameter dimension is large because it relies on user-chosen summary statistics rather than the full data and is therefore computationally feasible. One technical challenge with ABC is that the quality of the approximation to the posterior distribution of model parameters depends on the user-chosen summary statistics. In this paper, the user requirement to choose effective summary statistics in order to accurately estimate the posterior distribution of model parameters is investigated and illustrated by example, using a model and corresponding real data of mitochondrial DNA population dynamics. We show that for some choices of summary statistics, the posterior distribution of model parameters is closely approximated and for other choices of summary statistics, the posterior distribution is not closely approximated. A strategy to choose effective summary statistics is suggested in cases where the stochastic computer model can be run at many trial parameter settings, as in the example.