Slides of the workshop “Random Graphs in the Brain”.
In this talk a new class of stochastic processes is presented: the Hidden Context Tree Models (HCTM). This class gives a natural framework to mathematically address the neurobiological conjecture about the ability of the brain to identify the structure of a random source. Statistical model selection in a suitable subclass of HCTMs can provide experimental evidence supporting this conjecture. A case study with EEG data will be also presented. This is a joint work with A. Duarte, R. Fraiman, G. Ost and C. Vargas.
Slides of the First NeuroMat Young Researchers Workshop.
The aim of this presentation is to revise the functional regression models with scalar response (Linear, Nonlinear and Semilinear) and the extension to the more general case where the response belongs to the exponential family (binomial, poisson, gamma, ...). This extension allows to develop new functional classification methods based on this regression models. Some examples along with code implementation in R are provided during the talk. Lecturer: Manuel Febrero Bande, Univ. de Santiago de Compostela, Spain.
In this talk the topic of the goodness–of–fit for regression models with functional covariates is considered. Although several papers have been published in the last two decades for the checking of regression models, the case where the covariates are functional is quite recent and has became of interest in the last years. We will review the very recent advances in this area and we will propose a new goodness–of–fit test for the null hypothesis of a functional linear model with scalar response. Our test is based on a generalization to the functional framework of a previous one, designed for the goodness–of–fit of regression models with multivariate covariates using random projections. The test statistic is easy to compute using geometrical and matrix arguments, and simple to calibrate in its distribution by a wild bootstrap on the residuals. Some theoretical aspects are derived and the finite sample properties of the test are illustrated by a simulation study. Finally, the test is applied to real data for checking the assumption of the functional linear model and a graphical tool is introduced. Lecturer: Wenceslao González-Manteiga, Univ. de Santiago de Compostela, Spain.