Exact Bayesian inference for Markov switching Cox processes
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFMG |
Texto Completo: | http://hdl.handle.net/1843/33569 |
Resumo: | Statistical modelling of point patterns is an important and common problem in several areas. Poisson process is the most common process used for this purpose and, in particular, its generalisation considers a stochastic intensity function. This is called a Cox process and different choices to model the dynamics of the intensity give raise to a wide range of flexible models. We present a new class of unidimensional Cox processes in which the intensity function is driven by parametric functional forms that switch among themselves according to a continuous-time Markov chain. We refer to these as Markov switching Cox processes (MSCP). Previous developments in the literature are used to develop a Bayesian methodology to perform exact inference based on MCMC algorithms. The reliability of the algorithm depends on a variety of specifications which are carefully addressed. Simulated and real studies are presented in order to investigate the efficiency and applicability of the proposed methodology. |
id |
UFMG_184cc10fb3f994fa9333de15cdcf385c |
---|---|
oai_identifier_str |
oai:repositorio.ufmg.br:1843/33569 |
network_acronym_str |
UFMG |
network_name_str |
Repositório Institucional da UFMG |
repository_id_str |
|
spelling |
Flávio Bambirra Gonçalveshttp://lattes.cnpq.br/2015101359463631Roger William Câmara SilvaDani GamermanMarcos Oliveira PratesRafael IzbickiDaiane Aparecida Zuanettihttp://lattes.cnpq.br/0307283677820076Lívia Maria Dutra2020-05-29T19:18:58Z2020-05-29T19:18:58Z2019-12-04http://hdl.handle.net/1843/33569Statistical modelling of point patterns is an important and common problem in several areas. Poisson process is the most common process used for this purpose and, in particular, its generalisation considers a stochastic intensity function. This is called a Cox process and different choices to model the dynamics of the intensity give raise to a wide range of flexible models. We present a new class of unidimensional Cox processes in which the intensity function is driven by parametric functional forms that switch among themselves according to a continuous-time Markov chain. We refer to these as Markov switching Cox processes (MSCP). Previous developments in the literature are used to develop a Bayesian methodology to perform exact inference based on MCMC algorithms. The reliability of the algorithm depends on a variety of specifications which are carefully addressed. Simulated and real studies are presented in order to investigate the efficiency and applicability of the proposed methodology.A modelagem estatística de dados pontuais é um problema comum e importante em diversas áreas do conhecimento. O processo pontual mais amplamente utilizado e o mais comum é o processo de Poisson e, em particular, em uma de suas generalizações, sua função de intensidade é considerada também como um processo estocástico. Este modelo é conhecido como processo de Cox e diferentes opções para modelar a dinâmica da função de intensidade dão origem a uma ampla gama de modelos. Apresentamos uma nova classe de processos Cox unidimensionais, a qual é um processo de Poisson não-homogêneo em que a função de intensidade se alterna entre diferentes formas funcionais paramétricas de acordo com a trajetória de uma cadeia de Markov em tempo contínuo. Nos referimos a essa nova classe como processos de Cox com mudanças markovianas. Alguns resultados e algoritmos já presentes na literatura são utilizados como base para desenvolver uma metodologia Bayesiana para se realizar inferência exata, através de algoritmos MCMC. A confiabilidade do algoritmo depende de uma variedade de especificações que são cuidadosamente abordadas. Estudos simulados e análise de dados reais são apresentados com o objetivo de investigar a eficiência e aplicabilidade da metodologia proposta.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em EstatísticaUFMGBrasilICX - DEPARTAMENTO DE ESTATÍSTICAEstatística - TesesTeoria bayesiana de decisão estatísticaMarkov, Processos deBayesian inferenceExact posterior distributionsCox processContinuous-time Markov chainExact Bayesian inference for Markov switching Cox processesInferência Bayesiana exata para processos de Cox com mudanças markovianasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALExact Bayesian inference for Markov switching Cox processes.pdfExact Bayesian inference for Markov switching Cox processes.pdfapplication/pdf4110118https://repositorio.ufmg.br/bitstream/1843/33569/1/Exact%20Bayesian%20inference%20for%20Markov%20switching%20Cox%20processes.pdf850107a3d915fbfafbabbac021ce6f7bMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-82119https://repositorio.ufmg.br/bitstream/1843/33569/2/license.txt34badce4be7e31e3adb4575ae96af679MD521843/335692020-05-29 16:18:58.447oai:repositorio.ufmg.br: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Repositório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2020-05-29T19:18:58Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false |
dc.title.pt_BR.fl_str_mv |
Exact Bayesian inference for Markov switching Cox processes |
dc.title.alternative.pt_BR.fl_str_mv |
Inferência Bayesiana exata para processos de Cox com mudanças markovianas |
title |
Exact Bayesian inference for Markov switching Cox processes |
spellingShingle |
Exact Bayesian inference for Markov switching Cox processes Lívia Maria Dutra Bayesian inference Exact posterior distributions Cox process Continuous-time Markov chain Estatística - Teses Teoria bayesiana de decisão estatística Markov, Processos de |
title_short |
Exact Bayesian inference for Markov switching Cox processes |
title_full |
Exact Bayesian inference for Markov switching Cox processes |
title_fullStr |
Exact Bayesian inference for Markov switching Cox processes |
title_full_unstemmed |
Exact Bayesian inference for Markov switching Cox processes |
title_sort |
Exact Bayesian inference for Markov switching Cox processes |
author |
Lívia Maria Dutra |
author_facet |
Lívia Maria Dutra |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Flávio Bambirra Gonçalves |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/2015101359463631 |
dc.contributor.advisor-co1.fl_str_mv |
Roger William Câmara Silva |
dc.contributor.referee1.fl_str_mv |
Dani Gamerman |
dc.contributor.referee2.fl_str_mv |
Marcos Oliveira Prates |
dc.contributor.referee3.fl_str_mv |
Rafael Izbicki |
dc.contributor.referee4.fl_str_mv |
Daiane Aparecida Zuanetti |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/0307283677820076 |
dc.contributor.author.fl_str_mv |
Lívia Maria Dutra |
contributor_str_mv |
Flávio Bambirra Gonçalves Roger William Câmara Silva Dani Gamerman Marcos Oliveira Prates Rafael Izbicki Daiane Aparecida Zuanetti |
dc.subject.por.fl_str_mv |
Bayesian inference Exact posterior distributions Cox process Continuous-time Markov chain |
topic |
Bayesian inference Exact posterior distributions Cox process Continuous-time Markov chain Estatística - Teses Teoria bayesiana de decisão estatística Markov, Processos de |
dc.subject.other.pt_BR.fl_str_mv |
Estatística - Teses Teoria bayesiana de decisão estatística Markov, Processos de |
description |
Statistical modelling of point patterns is an important and common problem in several areas. Poisson process is the most common process used for this purpose and, in particular, its generalisation considers a stochastic intensity function. This is called a Cox process and different choices to model the dynamics of the intensity give raise to a wide range of flexible models. We present a new class of unidimensional Cox processes in which the intensity function is driven by parametric functional forms that switch among themselves according to a continuous-time Markov chain. We refer to these as Markov switching Cox processes (MSCP). Previous developments in the literature are used to develop a Bayesian methodology to perform exact inference based on MCMC algorithms. The reliability of the algorithm depends on a variety of specifications which are carefully addressed. Simulated and real studies are presented in order to investigate the efficiency and applicability of the proposed methodology. |
publishDate |
2019 |
dc.date.issued.fl_str_mv |
2019-12-04 |
dc.date.accessioned.fl_str_mv |
2020-05-29T19:18:58Z |
dc.date.available.fl_str_mv |
2020-05-29T19:18:58Z |
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/1843/33569 |
url |
http://hdl.handle.net/1843/33569 |
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 |
instname_str |
Universidade Federal de Minas Gerais (UFMG) |
instacron_str |
UFMG |
institution |
UFMG |
reponame_str |
Repositório Institucional da UFMG |
collection |
Repositório Institucional da UFMG |
bitstream.url.fl_str_mv |
https://repositorio.ufmg.br/bitstream/1843/33569/1/Exact%20Bayesian%20inference%20for%20Markov%20switching%20Cox%20processes.pdf https://repositorio.ufmg.br/bitstream/1843/33569/2/license.txt |
bitstream.checksum.fl_str_mv |
850107a3d915fbfafbabbac021ce6f7b 34badce4be7e31e3adb4575ae96af679 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG) |
repository.mail.fl_str_mv |
|
_version_ |
1803589424218374144 |