Space and Space-Time Models for Large Datasets

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In this project the investigator focuses on linear representations ofGaussian random fields. He considers models that either avoid explicitcomputation of the covariance matrix or do so for relatively smalldimensions. The correlation functions of the considered processes arevery general, avoiding particular symmetries or stationarity. The PIconsiders models that work in domains of general dimension and, inparticular, on the sphere, for gridded and non-gridded data. The PI useshierarchical methods of inference to account for measurement errors anddifferent sources of information. He develops statistically rigorousprocedures to summarize the information of dynamically evolving randomfields in a reduced number of time series and designs fast Monte Carlomethods that take advantage of parallel architectures.The investigator studies statistical models for spatial andspatio-temporal processes observed at a large number of locations andtime steps. The PI's research addresses the need for increasinglysophisticated models that can deal with different sources ofinformation, include expert opinion and handle effectively severalsources of uncertainty. While operating on large datasets, the PI'smodels consider time evolving dynamics and spatial heterogeneity.This allows for the analysis of phenomena on global scales, making gooduse of state of the art inferential and computational methods. Anexample of a problem where unified inferences from a variety of datasources is needed is the prediction of future climate from differentclimate models. Climate change prediction currently has a large societalimpact. This research provides tools to enhance our quantitativeunderstanding of the uncertainties involved in such predictions. Thiswill improve the ability of decision makers to make quality policydecisions.