The development of statistical methodology and computational techniques for the modelling of complex ecological data

This research proposal centers on the development of statistical methodology for data exhibiting spatial and/or*temporal dependencies with a particular interest in what is important for ecology.*State-space models (SSMs) are becoming standard tools for the analysis of animal tracking data and yet can be computationally intensive and difficult to implement, particularly when parameter estimation is involved. Particle Filter methods in MATLAB are proposed to implement SSMs for tracking data thereby a) greatly facilitating the integration of complex environmental data, b) enabling online fitting and c) allowing estimation of time-varying parameters via state augmentation. SSMs will then be far more accessible to ecologists, making it possible to ask important questions about how animals move in relation to their environment. *Generalized Additive Models (GAMs) are becoming very popular tools for analyzing ecological data and yet can be very sensitive to the presence of observations that deviate from the assumed model. First a formal comparison of the two popular approaches for fitting GAMs in R (mgcv and gam) will be carried out with particular attention to issues related to both robustness and ecological data. Improvements will then be made to mgcv so as to provide robust point estimates for the model parameters, as well as robustly obtained smoothing parameters. A new way of computing confidence intervals for the parameters that avoids the Bayesian approach available within mgcv will also be developed. Finally, issues including concurvity will be explored in an effort to make better tools available for performing model selection.*Clustered count data with excess zeros is typical of the sort of data collected on endangered species, particularly in marine environments. Random effect hurdle models that allow for possibly overlapping sets of covariates for each part of the model as well as the prediction of cluster-specific targets will be developed. These models will allow ecologists to answer critical questions related to expected abundance.*