Approximate Bayesian Inference for Individual-based Models with Emergent Dynamics

Abstract

Individual-based models are used in a variety of scientific domains to study systems composed of multiple agents that interact with one another and lead to complex emergent dynamics at the macroscale. A standard approach in the analysis of these systems is to specify the microscale interaction rules in a simulation model, run simulations, and then qualitatively compare outputs to empirical observations. Recently, more robust methods for inference for these types of models have been introduced, notably approximate Bayesian computation, however major challenges remain due to the computational cost of simulations and the nonlinear nature of many complex systems. Here, we compare two methods of approximate inference in a classic individual-based model of group dynamics with well-studied nonlinear macroscale behaviour; we employ a Gaussian process accelerated ABC method with an approximated likelihood and with a synthetic likelihood. We compare the accuracy of results when re-inferring parameters using a measure of macro-scale disorder (the order parameter) as a summary statistic. Our findings reveal that for a canonical simple model of animal collective movement, parameter inference is accurate and computationally efficient, even when the model is poised at the critical transition between order and disorder.