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Statistics seminar: Space-time tapers for covariance functions

Start Date: February 4, 2015
End Date: February 4, 2015

Professor Emilio Porcu, Department of Mathematics - University Federico Santa Maria, Chile

 
We propose a class of nonseparable space-time compactly supported correlation functions, termed here adaptive tapers, to mean that such correlations can be dynamically compactly supported over space or time. An important feature of the adaptive taper is given by a spatial (temporal) compact support being a decreasing function of the temporal lag (spatial distance), so that the spatial (temporal) compact support becomes smaller when the temporal (spatial) dependence becomes weaker. We propose general classes as well as some examples that generalize the Wendland tapers to the space-time setting. Then a nonseparable space-time adaptive taper with spatial and temporal compact support is obtained as tensor product of adaptive tapers. Our adaptive tapers include all the known constructions as special cases and are shown to have great exibility. Covariance tapering is then explored as an alternative to maximum likelihood when estimating the covariance model of a space-time Gaussian random field in the case of large datasets. The proposed adaptive and space-time adaptive tapers allow to perform covariance tapering when dealing with data that are densely observed in time (space) but sparsely in space(time), or densely observed in both time and space. The statistical and computational properties of the space-time adaptive covariance tapering is addressed under increasing domain asymptotics. A simulation study and two real data examples illustrate the statistical and computational per-formances of the covariance tapering with respect to the maximum likelihood method using the proposed space-time adaptive tapers. The talks is based on joint work with M. Bevilacqua, M. Genton, and V. P. Zastavnyi


Biography: Emilio Porcu did his PhD at the University of Milán and studied geostatistics at the Ecole des Mines de Paris. He has been working in Italy, Spain, Germany and now he is a professor at the University Federico Santa Maria in Chile. His other interests are in: Statistics and stochastic processes; with applications to Atmospheric, Environmental and Earth Sciences, Petroleum Engineering, and Economics, among other disciplines; space–time processes, geostatistics, point processes; Mathematics: Positive definite functions; variograms; completely monotone functions, locally compact Abelian Groups, Laplace transforms, potential theory. Recently, he has coined a discipline called Seismomatics to denote the fusion of mathematics, statistics, data mining for helping those discipline interested in the analysis and forecast of natural catastrophes, under the paradigm of Random Fields Theory. Special emphasis is put on analysis and assessment of earthquakes, tsunamis, avalanches, floodings, atmospheric and water pollution, and many other phenomena of interest for the health of the human being and for the economy of the countries. You can find more info about him, his research and his group at eporcu.mat.utfsm.cl

More Information:

Contact person for more info: Professor Marc Genton ; E-mail address: Marc.Genton@KAUST.EDU.SA

Location: Bldg.1, East side, spine level – MPR
Time: 15: 00 - 16: 00
Refreshments will be available at 14:45