Untitled - UFRJ

Bayesian Inference for Aggregated Functional Data withApplications to Electrical Data and ChemometricsNancy L. GarciaIMECC - Universidade Estadual de CampinasIn this work we address the problem of estimating mean curves when the available sample consists onaggregated functional data. Consider a typical curve for several sub-populations. Suppose that to samplefrom these individual curves is impossible (or too expensive). However, it is relatively easy to combinethese sub-populations and obtain sums of curves or weighted sums of curves. More specifically, replicatesof these curves are available and observations are made for “times” t=1,...,T. Our model specifies thatthe observed data is decomposed as the sum, over the C sub-populations, of latent structures whichare independent across sub-populations but temporally correlated. And these latent structures can bemodeled by Gaussian processes whose mean is a smooth curve depending on the sub-population andevolve with time t. Inference procedure is performed following the Bayesian paradigm. We apply ourmodel to a real dataset composed of the electric load of transformers which distributes energy to differenttypes of consumers and chemometric data obtained by Near-infrared (NIR) spectroscopy.Keywords: functional data, aggregated data, basis expansion, electric load monitoring, calibration,Near-infrared (NIR) spectroscopy14