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Extensions of hierarchical models, penalized regression, reference priors and functional data analysis

Grant number: 19/10800-0
Support type:Research Grants - Visiting Researcher Grant - Brazil
Duration: August 12, 2019 - August 11, 2020
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics
Principal Investigator:Ronaldo Dias
Grantee:Ronaldo Dias
Visiting researcher: Helio dos Santos Migon
Visiting researcher institution: Universidade Federal do Rio de Janeiro (UFRJ). Instituto de Matemática (IM), Brazil
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:18/04654-9 - Time series, wavelets and high dimensional data, AP.TEM

Abstract

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)