Statistical inference based on information theory for pre-shape data
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/33519 |
Resumo: | An important branch at Multivariate Analysis is Statistical Shape Analysis (SSA). A common demand in SSA is to study the shape property over objects in images, called planar-shape. To quantify difference in planar-shape between distinct groups is crucial in several areas – such as biology, medical image analysis, among others – and we provide advances in this sense. This thesis assumes pre-shapes which are obtained from twodimensional objects follow the complex Bingham (CB) distribution, having like the most important particular case the complex Watson (CW) model. From numerical evidence we present in this thesis, statistical tests which are well-defined in the SSA literature may provide low empirical test power curves. In order to obtain new alternatives to overcome this issue, we use information theory measures; in particular, stochastic entropies and distances. These measures play an important role in statistical theory, specifically into estimation and hypothesis inference procedures under large samples. First, we propose new distance-based two-sample hypothesis tests for triangle mean shapes. Closed-form expressions for the Rényi, Kullback-Leibler (KL), Bhattacharyya and Hellinger distances for the CW distribution are derived. The performance of proposed tests is quantified and compared with that due to the F2 test (analysis-of-variance tailored to the SSA literature). Furthermore, we perform an application to real data. Second, we extend the first topic proposing new distance-based two-sample hypothesis tests (for both homogeneity and mean shape) for the CB distribution and landmarks number higher than three. We derive the Rényi and KL divergences and the Bhattacharyya and Hellinger distances for the CB distribution. Three from among them may also be used like tests between two mean shapes or as discrepancy measures between the CB models. We prove also that the KL discrepancy for the CB model is rotation invariant. In order to evaluate and compare our proposals with other four SSA mean shape tests, a simulation study is also made to evaluate asymptotic and robustness properties. Finally an application in evolutionary biology is made. Third we tackle the proposal of new entropy-based multi-sample tests for variability in planar-shape. We develop closed-form expressions for the Rényi and Shannon entropies at the CB and CW models. From these quantities, hypothesis tests are obtained to assess if multiple spherical samples have the same degree of disorder. |
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FÉLIX, Wenia Valdevinohttp://lattes.cnpq.br/5246491774018325http://lattes.cnpq.br/9853084384672692NASCIMENTO, Abraão David Costa doAMARAL, Getulio Jose Amorim do2019-09-23T19:44:12Z2019-09-23T19:44:12Z2019-02-27https://repositorio.ufpe.br/handle/123456789/33519An important branch at Multivariate Analysis is Statistical Shape Analysis (SSA). A common demand in SSA is to study the shape property over objects in images, called planar-shape. To quantify difference in planar-shape between distinct groups is crucial in several areas – such as biology, medical image analysis, among others – and we provide advances in this sense. This thesis assumes pre-shapes which are obtained from twodimensional objects follow the complex Bingham (CB) distribution, having like the most important particular case the complex Watson (CW) model. From numerical evidence we present in this thesis, statistical tests which are well-defined in the SSA literature may provide low empirical test power curves. In order to obtain new alternatives to overcome this issue, we use information theory measures; in particular, stochastic entropies and distances. These measures play an important role in statistical theory, specifically into estimation and hypothesis inference procedures under large samples. First, we propose new distance-based two-sample hypothesis tests for triangle mean shapes. Closed-form expressions for the Rényi, Kullback-Leibler (KL), Bhattacharyya and Hellinger distances for the CW distribution are derived. The performance of proposed tests is quantified and compared with that due to the F2 test (analysis-of-variance tailored to the SSA literature). Furthermore, we perform an application to real data. Second, we extend the first topic proposing new distance-based two-sample hypothesis tests (for both homogeneity and mean shape) for the CB distribution and landmarks number higher than three. We derive the Rényi and KL divergences and the Bhattacharyya and Hellinger distances for the CB distribution. Three from among them may also be used like tests between two mean shapes or as discrepancy measures between the CB models. We prove also that the KL discrepancy for the CB model is rotation invariant. In order to evaluate and compare our proposals with other four SSA mean shape tests, a simulation study is also made to evaluate asymptotic and robustness properties. Finally an application in evolutionary biology is made. Third we tackle the proposal of new entropy-based multi-sample tests for variability in planar-shape. We develop closed-form expressions for the Rényi and Shannon entropies at the CB and CW models. From these quantities, hypothesis tests are obtained to assess if multiple spherical samples have the same degree of disorder.CAPESUm ramo importante na Análise Multivariada é a Análise Estatística da Forma (AEF). Uma demanda comum em AEF é estudar propriedades de forma sobre objetos em imagens, chamada forma-planar. Quantificar diferenças em forma-planar entre grupos distintos é crucial em várias áreas – tais como biologia, análise de imagens médicas e outras – e nós apresentamos avanços neste sentido. Esta tese pressupõe que pré-formas obtidas a partir de objetos bidimensionais seguem a distribuição Bingham complexa (CB), tendo como o mais importante caso particular o modelo Watson complexo (CW). A partir de evidências numéricas que apresentamos nesta tese, testes bem definidos na literatura da AEF podem fornecer baixas curvas empíricas para o poder do teste. A fim de obter novas alternativas para superar este problema, usamos medidas da Teoria da Informação; em particular, entropias e distâncias estocásticas. Essas medidas desempenham um papel importante na teoria estatística, especificamente nos procedimentos de inferência por estimação e hipóteses em grandes amostras. Primeiro, propomos novos testes de hipóteses de duas amostras baseados em distâncias para formas médias de triângulo. Expressões em forma fechada para as distâncias de Rényi, Kullback-Leibler (KL), Bhattacharyya e Hellinger para a distribuição CW são derivadas. O desempenho dos testes propostos é quantificado e comparado com o teste F2 (análise de variância adaptada à literatura de AEF). Além disso, realizamos uma aplicação a dados reais. Em segundo lugar, estendemos o primeiro tópico propondo novos testes de hipóteses de duas amostras baseados em distância (tanto para homogeneidade quanto para forma média) para a distribuição CB e número de pontos de referência maior que três. Derivamos as divergências de Rényi e KL e as distâncias de Bhattacharyya e Hellinger para a distribuição CB. Três dentre elas também podem ser usadas como testes entre duas formas médias ou como medidas de discrepância entre modelos CB. Provamos também que a divergência KL para o modelo CB é invariante à rotação. Para avaliar e comparar as nossas propostas com outros quatro testes de forma média em AEF, também é feito um estudo de simulação para avaliar propriedades assintóticas e de robustez. Finalmente, uma aplicação em biologia da evolução é feita. Em terceiro lugar, abordamos a proposta de novos testes de múltiplas amostras baseados em entropia para a variabilidade em forma-planar. Desenvolvemos expressões em forma fechada para as entropias de Rényi e Shannon nos modelos CB e CW. A partir dessas quantidades, testes de hipóteses são obtidos para avaliar se múltiplas amostras esféricas têm o mesmo grau de desordem.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em EstatisticaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessEstatísticaDistâncias estocásticasStatistical inference based on information theory for pre-shape datainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILTESE Wenia Valdevino Félix.pdf.jpgTESE Wenia Valdevino Félix.pdf.jpgGenerated Thumbnailimage/jpeg1393https://repositorio.ufpe.br/bitstream/123456789/33519/5/TESE%20Wenia%20Valdevino%20F%c3%a9lix.pdf.jpge5c4f65a98a52c603f0262a0bff2b1a7MD55ORIGINALTESE Wenia Valdevino Félix.pdfTESE Wenia Valdevino Félix.pdfapplication/pdf2442546https://repositorio.ufpe.br/bitstream/123456789/33519/1/TESE%20Wenia%20Valdevino%20F%c3%a9lix.pdf665e117ac590de685b6be61306b2b717MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv |
Statistical inference based on information theory for pre-shape data |
title |
Statistical inference based on information theory for pre-shape data |
spellingShingle |
Statistical inference based on information theory for pre-shape data FÉLIX, Wenia Valdevino Estatística Distâncias estocásticas |
title_short |
Statistical inference based on information theory for pre-shape data |
title_full |
Statistical inference based on information theory for pre-shape data |
title_fullStr |
Statistical inference based on information theory for pre-shape data |
title_full_unstemmed |
Statistical inference based on information theory for pre-shape data |
title_sort |
Statistical inference based on information theory for pre-shape data |
author |
FÉLIX, Wenia Valdevino |
author_facet |
FÉLIX, Wenia Valdevino |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/5246491774018325 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/9853084384672692 |
dc.contributor.author.fl_str_mv |
FÉLIX, Wenia Valdevino |
dc.contributor.advisor1.fl_str_mv |
NASCIMENTO, Abraão David Costa do |
dc.contributor.advisor-co1.fl_str_mv |
AMARAL, Getulio Jose Amorim do |
contributor_str_mv |
NASCIMENTO, Abraão David Costa do AMARAL, Getulio Jose Amorim do |
dc.subject.por.fl_str_mv |
Estatística Distâncias estocásticas |
topic |
Estatística Distâncias estocásticas |
description |
An important branch at Multivariate Analysis is Statistical Shape Analysis (SSA). A common demand in SSA is to study the shape property over objects in images, called planar-shape. To quantify difference in planar-shape between distinct groups is crucial in several areas – such as biology, medical image analysis, among others – and we provide advances in this sense. This thesis assumes pre-shapes which are obtained from twodimensional objects follow the complex Bingham (CB) distribution, having like the most important particular case the complex Watson (CW) model. From numerical evidence we present in this thesis, statistical tests which are well-defined in the SSA literature may provide low empirical test power curves. In order to obtain new alternatives to overcome this issue, we use information theory measures; in particular, stochastic entropies and distances. These measures play an important role in statistical theory, specifically into estimation and hypothesis inference procedures under large samples. First, we propose new distance-based two-sample hypothesis tests for triangle mean shapes. Closed-form expressions for the Rényi, Kullback-Leibler (KL), Bhattacharyya and Hellinger distances for the CW distribution are derived. The performance of proposed tests is quantified and compared with that due to the F2 test (analysis-of-variance tailored to the SSA literature). Furthermore, we perform an application to real data. Second, we extend the first topic proposing new distance-based two-sample hypothesis tests (for both homogeneity and mean shape) for the CB distribution and landmarks number higher than three. We derive the Rényi and KL divergences and the Bhattacharyya and Hellinger distances for the CB distribution. Three from among them may also be used like tests between two mean shapes or as discrepancy measures between the CB models. We prove also that the KL discrepancy for the CB model is rotation invariant. In order to evaluate and compare our proposals with other four SSA mean shape tests, a simulation study is also made to evaluate asymptotic and robustness properties. Finally an application in evolutionary biology is made. Third we tackle the proposal of new entropy-based multi-sample tests for variability in planar-shape. We develop closed-form expressions for the Rényi and Shannon entropies at the CB and CW models. From these quantities, hypothesis tests are obtained to assess if multiple spherical samples have the same degree of disorder. |
publishDate |
2019 |
dc.date.accessioned.fl_str_mv |
2019-09-23T19:44:12Z |
dc.date.available.fl_str_mv |
2019-09-23T19:44:12Z |
dc.date.issued.fl_str_mv |
2019-02-27 |
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 |
https://repositorio.ufpe.br/handle/123456789/33519 |
url |
https://repositorio.ufpe.br/handle/123456789/33519 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Estatistica |
dc.publisher.initials.fl_str_mv |
UFPE |
dc.publisher.country.fl_str_mv |
Brasil |
publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.source.none.fl_str_mv |
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