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Analysis of spatio-temporal aggregated data

Grant number: 14/26419-0
Support type:Scholarships abroad - Research
Effective date (Start): August 15, 2015
Effective date (End): July 15, 2016
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
Principal researcher:Nancy Lopes Garcia
Grantee:Nancy Lopes Garcia
Host: Peter Guttorp
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Research place: University of Washington, United States  


n many areas of science one aims to study latent sub-population based only on observations of aggregated population observation. In this work, aggregated curves will mean linear combination of functional data that cannot be observed individually. We assume that several aggregated curves with linearly independent coefficients are available and each aggregated curve is an independent partial realization of aGaussian process with mean modeled through a weighted linearcombination of the disaggregated curves. In the univariate setup, the estimation of the mean curves was studied in several previous works by the author. Another important question is the estimation of the covariance function. Differently from the estimation of the mean curves, which tend to be very good, the estimation of the covariance functions deserves further investigation. If there is no replication for the aggregated curveswith the same coefficients, simulation studies under the Bayesianframework showed the difficulty in estimating the covariance functions for the sub-populations in the non-stationary case. Moreover, it involves an additional difficulty, the resulting functions have to be positive definite. Some alternative methods for the estimation of covariance function in the univariate setup have been developed in a work in progress. During the visit to the Department of Statistics at University ofWashington, we propose to work jointly with Peter Guttorp togeneralize the above mentioned works for the study aggregated surfaces and aggregated spatiotemporal processes. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
GALLO, SANDRO; GARCIA, NANCY L.. Discrete One-Dimensional Coverage Process on a Renewal Process. Journal of Statistical Physics, v. 173, n. 2, p. 381-397, . (14/26419-0, 17/07084-6, 15/09094-3, 13/07699-0)
LENZI, AMANDA; DE SOUZA, CAMILA P. E.; DIAS, RONALDO; GARCIA, NANCY L.; HECKMAN, NANCY E.. Analysis of aggregated functional data from mixed populations with application to energy consumption. ENVIRONMETRICS, v. 28, n. 2, . (13/07375-0, 14/26419-0, 14/26414-9)
GARCIA, NANCY L.; GUTTORP, PETER; LUDWIG, GUILHERME. Interacting cluster point process model for epidermal nerve fibers. SPATIAL STATISTICS, v. 35, . (14/26419-0, 16/09390-4, 18/09877-6, 17/15306-9)

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