Complex simulation models are being increasingly used in ecological modelling as a way of trying to understand a system by examining the processes that make up that system. Complex simulation models generally model behaviour of a system through a series of rules or algorithms, rather than describing it in a formal mathematical way and this can be a good way of capturing an ecologist's expertise and intuition. When interpreting outputs from such a model, it is important to allow for uncertainty due to parameter values which may not be known precisely and structural or implementation aspects. This thesis develops and applies a number of new statistical methods for handling uncertainty in such models.
For stochastic simulation models with intractable likelihoods, parameter estimation can be done using Approximate Bayesian Computation with Markov Chain Monte Carlo (ABC-MCMC). This method does not mix well in the tails of the distribution. In this thesis we develop a version of ABC-MCMC that treats the random inputs as unknown as well as the unknown model parameters and we show empirically that this improves the efficiency of the ABC-MCMC algorithm on a queuing model and an individual-based model (IBM) of the group-living bird, the woodhoopoe.
For models that are expensive to run, inference may be challenging even if the likelihood can be evaluated. We consider a deterministic multi-species size-based marine ecosystem model, with unknown initial states and parameters, and carry out Bayesian inference using a combination of MCMC and optimisation algorithms.
Stochastic simulation models, especially IBMs, often have model uncertainty that is down to some seemingly arbitrary choices, for example spatial or temporal scales, the timing of different events or the spatial configuration. Ideally the outputs of the model should be insensitive to these choices. We develop methods for variance-based sensitivity analysis for stochastic models, allowing us to assess the sensitivity of the model outputs to stochasticity of the inputs and to partition out the variance between submodels. This enables us to test the arbitrary choices made by the modeller and thus test the robustness of the model. We demonstrate these methods on two IBMs: the woodhoopoe model and a bird breeding synchrony model.
