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Extensions of Hierarchical Models, Penalized Regression, Reference Priors and Functional Data Analysis.


This research project deals with two central aspects in statistical modeling:inference and decision making. We often find ourselves, in nowadays, with high dimensional problems, both in the available data and in the number ofcovariates. Let p> n, where p is the number of covariates (features) and n, the numberof observations.These issues are increasingly present in useful statistical methodsfor Machine Learning involving Big Data.In Statistical Machine Learning it is commonestimating a non-linear function, known except for a parameter vector, which can be difficult some times. One way to extend and generalize this problem is to consider techniques such as non-parametric estimation of curves. In order to achieve the described objectives, we will develop research on currentBayesian inference, with emphasis on methodological, computational and applied aspects.Our proposal is to address these problems in an integrated way and according to the same computational framework. Among our goals, we highlight this research in:i) Regularization and Selection of Models: penalized regression, penalized regressionfunctional.ii) Functional Data Modeling: extensions of hierarchical models.iii) Applications of Dynamic Hierarchical Models: a longitudinal data / survivaland epidemiological models. (AU)

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