Bayesian Inference on Individual-Based Models by Controlling the Random Inputs
Complex models are becoming increasingly popular in ecological modelling. However, quantifying uncertainty, estimating parameters and so on for a model of this sort are complicated by the fact that their probabilistic behaviour is often implicit in its ru
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Bayesian Inference on Individual-Based Models by Controlling the Random Inputs Michael Spence and Paul Blackwell
Abstract Complex models are becoming increasingly popular in ecological modelling. However, quantifying uncertainty, estimating parameters and so on for a model of this sort are complicated by the fact that their probabilistic behaviour is often implicit in its rules or programs rather than made explicit as in a more conventional statistical or stochastic model. In a complex stochastic model, the output is dependent on both the parameters and the random inputs, i.e. the random numbers used to resolve decisions or generate stochastic quantities within the model. By treating these random inputs as nuisance parameters, often we can turn the model into a deterministic model where small movements in the parameter space result in small changes in the model output. When this is the case it will allow us to use Approximate Bayesian Computation methods with MCMC in order to perform parameter estimation. Controlling the random inputs allows us to move better in the parameter space and improves the mixing of the Markov chain. We will use these methods to estimate parameters in an individual-based model which is used to model the population dynamics of a group-living bird, the woodhoopoe.
8.1 Introduction In ecology the need for answering the question “what makes something happen?” as opposed to “what actually happens?” is becoming increasingly popular. These questions lead to building complex models where the different aspects of the system
M. Spence () • P. Blackwell School of Mathematics and Statistics, University of Sheffield, Sheffield, UK e-mail: [email protected]; [email protected] E. Lanzarone and F. Ieva (eds.), The Contribution of Young Researchers to Bayesian Statistics, Springer Proceedings in Mathematics & Statistics 63, DOI 10.1007/978-3-319-02084-6__8, © Springer International Publishing Switzerland 2014
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are modelled separately and give rise to the collective behaviour of the system. A natural approach in ecology is to model each individual separately in the system. These are called individual-based models (IBMs) [5]. IBMs generally model behaviour through a series of rules or algorithms rather than describing it in a formal mathematical way. They are developed with algorithms that are not well tuned from the beginning but require parameters that are either not precise enough in the literature or simply not concretely measurable [6]. As the probabilistic behaviour of the model is implicit in the rules of the model, the likelihood is generally intractable. Using pattern-oriented methods [7], parameter values can be found indirectly by changing a number of parameters at once and seeing if the model output matches some observed data [9, 10]. As IBMs have many parameters that can have complex and interacting effects on the output, this approach may be unproductive [2] so other methods of parameter estimation are required. Current methods for per
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