Spatial analysis and visualization of global data on multi-resolution hexagonal grids.

In this article, computation for the purpose of spatial visualization is presented in the context of understanding the variability in global environmental processes. Here, we generate synthetic but realistic global data sets and input them into computational algorithms that have a visualization capability; we call this a simulation-visualization system. Visualization is key here, because the algorithms which we are evaluating must respect the spatial structure of the input.

Bayesian learning and predictability in a stochastic nonlinear dynamical model.

Bayesian inference methods are applied within a Bayesian hierarchical modeling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple nonlinear marine biogeochemical model. A novel approach is proposed to the formulation of the stochastic process model, in which ecophysiological properties of plankton communities are represented by autoregressive stochastic processes.

Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling.

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions.

Hierarchical statistical modelling of influenza epidemic dynamics in space and time.

An infectious disease typically spreads via contact between infected and susceptible individuals. Since the small-scale movements and contacts between people are generally not recorded, available data regarding infectious disease are often aggregations in space and time, yielding small-area counts of the number infected during successive, regular time intervals. In this paper, we develop a spatially descriptive, temporally dynamic hierarchical model to be fitted to such data.