New Statistical Methodologies
In the research subprojects, we outline a diverse array of complex marine environmental data in the context of outstanding research questions in marine ecology that can be addressed through the development and application of novel statistical techniques. Such techniques are needed to help us to explore and model relationships between the many diverse data types that will be linked in time and space on the same or different scales. Rather than propose a single, unifying methodology, we anticipate using a variety of statistical and modeling techniques that are tailored to the particular problems under consideration. These include: nonlinear time series models, state space models, Bayesian methods, spatial analysis, extreme value distributions, hierarchical models, nonlinear regression, and MCMC. We will also consider problems associated with model building, model selection, and robustness.
Nonlinear Ecological Time Series
In many of the situations of interest in marine ecology there is a large volume of multivariate spatial/temporal data, and a correspondingly large dimension for the ecological state space. An integral part of the statistical models will be the design and application of computational techniques to ensure that the appropriate inference can be carried out. Our aim is to ensure that our methodology can handle realistic data volumes and complexity both efficiently and effectively. In order to carry out validation of our models, and to do inference, we will have to rely on re-sampling techniques such as the bootstrap. Applications to these complex spatial/temporal models will require careful development.