Inferring the underlying processes that drive collective behaviour in biological and social systems is a significant statistical and computational challenge. While simulation models have been successful in qualitatively capturing many of the phenomena observed in these systems in a variety of domains, formally fitting these models to data remains intractable. Recently, approximate Bayesian computation (ABC) has been shown to be an effective approach to inference if the likelihood function for a model is unavailable. However, a key difficulty in successfully implementing ABC lies with the design, selection and weighting of appropriate summary statistics, a challenge that is especially acute when modelling high dimensional complex systems. In this work, we combine a Gaussian process accelerated ABC method with the automatic learning of summary statistics via graph neural networks. Our approach bypasses the need to design a model-specific set of summary statistics for inference. Instead, we encode relational inductive biases into a neural network using a graph embedding and then extract summary statistics automatically from simulation data. To evaluate our framework, we use a model of collective animal movement as a test bed and compare our method to a standard summary statistics approach and a linear regression-based algorithm.
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.
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