Bayesian inference for models of collective behaviour

Abstract

The study of collective behaviour—broadly defined as the formation of macro-level structures from the interactions between individuals—has in recent years become a thriving topic of multi-disciplinary research. Under consideration of biological- tness the scientist has been able to reason about why these structures form, and the advantages which the collective can afford the individual. However, much less is known about how these structures are formed and maintained in the first place. Much work has been invested in the development of mathematical models which seek to explain the formation and maintenance of animal aggregations. Research has shown that behaviour reminiscent of real flocking events can arise from simple mathematical models which describe how individuals interact with one another. However,much of this modelling relies on aprioristic assumptions about how individuals behave and interact, with little-to-no verification against real observation. In this work we examine mathematical models popular in the literature and suggest modifications motivated by considerations of biological-realism. In particular we advocate adoption of continuous interaction rules, and consider how behavioural and biological variation can be accounted for by imposing hierarchical structure. We proceed to fit these models of collective behaviour to observations of real and simulated flocking events. Model tting is performed in a Bayesian framework, allowing the quantification of parameter uncertainty. Fitting models to simulated data provides opportunity to assess the e ectiveness and accuracy of our inference schemes, before attempting the same inference on real observation. Multiple competing models are fit to the same data, with the predictive performance of these models ranked using ideas from the model-selection literature. We are then able to recommend a subset of the candidate models as providing the best performance. Finally, consideration is made for datasets which exhibit missing observations. Such missingness occurs naturally owing to the fixed-location recording equipment used to record flocking events. We argue that this missingness cannot be ignored, and must be accounted for during any model- fitting process. Techniques are outlined which allow the researcher to account for missingness. Simulation studies are performed which demonstrate the eficacy of the outlined approach, before the techniques are demonstrated on a real dataset exhibiting missingness.