In this project the investigator focuses on linear representations of Gaussian random fields. He considers models that either avoid explicit computation of the covariance matrix or do so for relatively small dimensions. The correlation functions of the considered processes are very general, avoiding particular symmetries or stationarity. The PI considers models that work in domains of general dimension and, in particular, on the sphere, for gridded and non-gridded data. The PI uses hierarchical methods of inference to account for measurement errors and different sources of information. He develops statistically rigorous procedures to summarize the information of dynamically evolving random fields in a reduced number of time series and designs fast Monte Carlo methods that take advantage of parallel architectures.
The investigator studies statistical models for spatial and spatio-temporal processes observed at a large number of locations and time steps. The PI's research addresses the need for increasingly sophisticated models that can deal with different sources of information, include expert opinion and handle effectively several sources of uncertainty. While operating on large datasets, the PI's models consider time evolving dynamics and spatial heterogeneity. This allows for the analysis of phenomena on global scales, making good use of state of the art inferential and computational methods. An example of a problem where unified inferences from a variety of data sources is needed is the prediction of future climate from different climate models. Climate change prediction currently has a large societal impact. This research provides tools to enhance our quantitative understanding of the uncertainties involved in such predictions. This will improve the ability of decision makers to make quality policy decisions.
