Functional data analysis: spatial association of curves and irregular spacing
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFMG |
Texto Completo: | http://hdl.handle.net/1843/59365 |
Resumo: | Spatial Functional Data (SFD) analysis is an emerging statistical framework that combines Functional Data Analysis (FDA) and spatial dependency modeling. Unlike traditional statistical methods, which treat data as scalar values or vectors, SFD considers data as continuous functions, allowing for a more comprehensive understanding of their behavior and variability. This approach is well-suited for analyzing data collected over time, space, or any other continuous domain. SFD has found applications in various fields, including economics, finance, medicine, environmental science, and engineering. This thesis proposes new functional Gaussian models incorporating spatial dependence structures, focusing on irregularly spaced data and reflecting spatially correlated curves. The models are based on B-spline basis expansions and Bernstein Polynomials (BP) and utilize a Bayesian approach for estimating unknown quantities and parameters. The thesis explores the advantages and limitations of B-spline-based and BP-based models in capturing complex shapes and patterns while ensuring numerical stability. The main contributions of this work include the development of an innovative model designed for SFD using B-spline or BP structures, including a random effect to address associations between irregularly spaced observations, and a comprehensive simulation study to evaluate models' performance under various scenarios. The thesis also presents two real applications related to levels of PM10 and Temperature in Mexico City, showcasing practical illustrations of the proposed models. |
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Vinícius Diniz Mayrinkhttp://lattes.cnpq.br/8460573638694827Flávio Bambirra GonçalvesMarcos Oliveira PratesAirlane Pereira AlencarRonaldo Diashttp://lattes.cnpq.br/5709479113381426Alvaro Alexander Burbano Moreno2023-10-10T18:14:13Z2023-10-10T18:14:13Z2023-09-12http://hdl.handle.net/1843/59365Spatial Functional Data (SFD) analysis is an emerging statistical framework that combines Functional Data Analysis (FDA) and spatial dependency modeling. Unlike traditional statistical methods, which treat data as scalar values or vectors, SFD considers data as continuous functions, allowing for a more comprehensive understanding of their behavior and variability. This approach is well-suited for analyzing data collected over time, space, or any other continuous domain. SFD has found applications in various fields, including economics, finance, medicine, environmental science, and engineering. This thesis proposes new functional Gaussian models incorporating spatial dependence structures, focusing on irregularly spaced data and reflecting spatially correlated curves. The models are based on B-spline basis expansions and Bernstein Polynomials (BP) and utilize a Bayesian approach for estimating unknown quantities and parameters. The thesis explores the advantages and limitations of B-spline-based and BP-based models in capturing complex shapes and patterns while ensuring numerical stability. The main contributions of this work include the development of an innovative model designed for SFD using B-spline or BP structures, including a random effect to address associations between irregularly spaced observations, and a comprehensive simulation study to evaluate models' performance under various scenarios. The thesis also presents two real applications related to levels of PM10 and Temperature in Mexico City, showcasing practical illustrations of the proposed models.A análise de dados funcionais espaciais (SFD) é um área da estatística emergente que combina a análise de dados funcionais (FDA) e a modelagem de dependência espacial. Diferentemente dos métodos estatísticos tradicionais que tratam os dados como valores escalares ou vetores, a SFD considera os dados como funções contínuas, permitindo uma compreensão mais completa de seu comportamento e variabilidade. Essa abordagem é adequada para analisar dados coletados ao longo do tempo, do espaço ou de qualquer outro domínio contínuo. A SFD é aplicada em vários campos, incluindo economia, finanças, medicina, ciências ambientais e engenharia. Esta tese propõe novos modelos funcionais Gaussianos que incorporam estruturas de dependência espacial, com foco em dados tendo espaçamento irregular e que refletem curvas espacialmente correlacionadas. Os modelos são baseados em expansões de base B-spline e Polinômios de Bernstein (BP) e utilizam uma abordagem Bayesiana para estimar quantidades e parâmetros desconhecidos. A tese explora as vantagens e limitações dos modelos baseados em B-spline e BP na captura de formas e padrões complexos, garantindo a estabilidade numérica. As principais contribuições deste trabalho incluem o desenvolvimento de um modelo inovador voltado para SFD usando estruturas B-spline ou BP, incluindo um efeito aleatório para tratar de associações entre observações com espaçamento irregular, e um estudo de simulação abrangente para avaliar o desempenho dos modelos em vários cenários. A tese também apresenta duas aplicações reais relacionadas aos níveis de PM10 e Temperatura na Cidade do México, demonstrando ilustrações práticas dos modelos propostos.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em EstatísticaUFMGBrasilICX - DEPARTAMENTO DE ESTATÍSTICAEstatística – TesesAnálise Espacial (Estatística) – TesesInferência Bayesiana – TesesProcessos Gaussianos – TesesSpline – TesesPolinômios de BernsteinB-splineBernstein polynomialsBayesian inferenceGaussian ProcessMCMCFunctional data analysis: spatial association of curves and irregular spacingAnálise de dados funcionais: associação espacial de curvas e espaçamento irregularinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALTese_Doutorado.pdfTese_Doutorado.pdfTese Doutorado Alvaro Alexander Burbano Morenoapplication/pdf13719860https://repositorio.ufmg.br/bitstream/1843/59365/1/Tese_Doutorado.pdfb8c71f709ce29bf868ced3e1cd5d124dMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/59365/2/license.txtcda590c95a0b51b4d15f60c9642ca272MD521843/593652023-10-10 15:14:13.692oai:repositorio.ufmg.br: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ório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2023-10-10T18:14:13Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false |
dc.title.pt_BR.fl_str_mv |
Functional data analysis: spatial association of curves and irregular spacing |
dc.title.alternative.pt_BR.fl_str_mv |
Análise de dados funcionais: associação espacial de curvas e espaçamento irregular |
title |
Functional data analysis: spatial association of curves and irregular spacing |
spellingShingle |
Functional data analysis: spatial association of curves and irregular spacing Alvaro Alexander Burbano Moreno B-spline Bernstein polynomials Bayesian inference Gaussian Process MCMC Estatística – Teses Análise Espacial (Estatística) – Teses Inferência Bayesiana – Teses Processos Gaussianos – Teses Spline – Teses Polinômios de Bernstein |
title_short |
Functional data analysis: spatial association of curves and irregular spacing |
title_full |
Functional data analysis: spatial association of curves and irregular spacing |
title_fullStr |
Functional data analysis: spatial association of curves and irregular spacing |
title_full_unstemmed |
Functional data analysis: spatial association of curves and irregular spacing |
title_sort |
Functional data analysis: spatial association of curves and irregular spacing |
author |
Alvaro Alexander Burbano Moreno |
author_facet |
Alvaro Alexander Burbano Moreno |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Vinícius Diniz Mayrink |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8460573638694827 |
dc.contributor.referee1.fl_str_mv |
Flávio Bambirra Gonçalves |
dc.contributor.referee2.fl_str_mv |
Marcos Oliveira Prates |
dc.contributor.referee3.fl_str_mv |
Airlane Pereira Alencar |
dc.contributor.referee4.fl_str_mv |
Ronaldo Dias |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/5709479113381426 |
dc.contributor.author.fl_str_mv |
Alvaro Alexander Burbano Moreno |
contributor_str_mv |
Vinícius Diniz Mayrink Flávio Bambirra Gonçalves Marcos Oliveira Prates Airlane Pereira Alencar Ronaldo Dias |
dc.subject.por.fl_str_mv |
B-spline Bernstein polynomials Bayesian inference Gaussian Process MCMC |
topic |
B-spline Bernstein polynomials Bayesian inference Gaussian Process MCMC Estatística – Teses Análise Espacial (Estatística) – Teses Inferência Bayesiana – Teses Processos Gaussianos – Teses Spline – Teses Polinômios de Bernstein |
dc.subject.other.pt_BR.fl_str_mv |
Estatística – Teses Análise Espacial (Estatística) – Teses Inferência Bayesiana – Teses Processos Gaussianos – Teses Spline – Teses Polinômios de Bernstein |
description |
Spatial Functional Data (SFD) analysis is an emerging statistical framework that combines Functional Data Analysis (FDA) and spatial dependency modeling. Unlike traditional statistical methods, which treat data as scalar values or vectors, SFD considers data as continuous functions, allowing for a more comprehensive understanding of their behavior and variability. This approach is well-suited for analyzing data collected over time, space, or any other continuous domain. SFD has found applications in various fields, including economics, finance, medicine, environmental science, and engineering. This thesis proposes new functional Gaussian models incorporating spatial dependence structures, focusing on irregularly spaced data and reflecting spatially correlated curves. The models are based on B-spline basis expansions and Bernstein Polynomials (BP) and utilize a Bayesian approach for estimating unknown quantities and parameters. The thesis explores the advantages and limitations of B-spline-based and BP-based models in capturing complex shapes and patterns while ensuring numerical stability. The main contributions of this work include the development of an innovative model designed for SFD using B-spline or BP structures, including a random effect to address associations between irregularly spaced observations, and a comprehensive simulation study to evaluate models' performance under various scenarios. The thesis also presents two real applications related to levels of PM10 and Temperature in Mexico City, showcasing practical illustrations of the proposed models. |
publishDate |
2023 |
dc.date.accessioned.fl_str_mv |
2023-10-10T18:14:13Z |
dc.date.available.fl_str_mv |
2023-10-10T18:14:13Z |
dc.date.issued.fl_str_mv |
2023-09-12 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1843/59365 |
url |
http://hdl.handle.net/1843/59365 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Estatística |
dc.publisher.initials.fl_str_mv |
UFMG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
ICX - DEPARTAMENTO DE ESTATÍSTICA |
publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFMG instname:Universidade Federal de Minas Gerais (UFMG) instacron:UFMG |
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UFMG |
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UFMG |
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Repositório Institucional da UFMG |
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Repositório Institucional da UFMG |
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