Exact Bayesian inference for Markov switching Cox processes

Detalhes bibliográficos
Ano de defesa: 2015
Autor(a) principal: Livia Maria Dutra
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: eng
Instituição de defesa: Universidade Federal de Minas Gerais
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Estatística
Markov, processos de
Teoria bayesiana de decisão estatistica
Link de acesso: https://hdl.handle.net/1843/BUBD-9WGFNQ
Resumo: Statistical modelling of point patterns is an important and common problem in several applications. An important point process, and a generalisation of the Poisson process, is the Cox process, where the intensity function is itself stochastic. We focus on Cox processes in which the intensity function is driven by a nite state space continuous-time Markov chain. We refer to these as Markov switching Cox processes (MSCP). We investigate some probabilistic properties of these processes, three new theorems for these processes are derived and we develop a Bayesian methodology to perform exact inference based on MCMC algorithms. Since the likelihood function is tractable, it facilitates the development of an exact methodology. Simulated studies are presented in order to investigate the efficiency of the methodology on the estimation of MSCP's intensity function and the parameters indexing its law. Finally, an analysis with real data is performed.
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spelling Exact Bayesian inference for Markov switching Cox processesEstatísticaMarkov, processos deTeoria bayesiana de decisão estatisticaEstatísticaStatistical modelling of point patterns is an important and common problem in several applications. An important point process, and a generalisation of the Poisson process, is the Cox process, where the intensity function is itself stochastic. We focus on Cox processes in which the intensity function is driven by a nite state space continuous-time Markov chain. We refer to these as Markov switching Cox processes (MSCP). We investigate some probabilistic properties of these processes, three new theorems for these processes are derived and we develop a Bayesian methodology to perform exact inference based on MCMC algorithms. Since the likelihood function is tractable, it facilitates the development of an exact methodology. Simulated studies are presented in order to investigate the efficiency of the methodology on the estimation of MSCP's intensity function and the parameters indexing its law. Finally, an analysis with real data is performed.Universidade Federal de Minas Gerais2019-08-11T02:06:53Z2025-09-09T00:50:39Z2019-08-11T02:06:53Z2015-03-02info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/1843/BUBD-9WGFNQLivia Maria Dutrainfo:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMG2025-09-09T00:50:39Zoai:repositorio.ufmg.br:1843/BUBD-9WGFNQRepositório InstitucionalPUBhttps://repositorio.ufmg.br/oairepositorio@ufmg.bropendoar:2025-09-09T00:50:39Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
dc.title.none.fl_str_mv Exact Bayesian inference for Markov switching Cox processes
title Exact Bayesian inference for Markov switching Cox processes
spellingShingle Exact Bayesian inference for Markov switching Cox processes
Livia Maria Dutra
Estatística
Markov, processos de
Teoria bayesiana de decisão estatistica
Estatística
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 Livia Maria Dutra
author_facet Livia Maria Dutra
author_role author
dc.contributor.author.fl_str_mv Livia Maria Dutra
dc.subject.por.fl_str_mv Estatística
Markov, processos de
Teoria bayesiana de decisão estatistica
Estatística
topic Estatística
Markov, processos de
Teoria bayesiana de decisão estatistica
Estatística
description Statistical modelling of point patterns is an important and common problem in several applications. An important point process, and a generalisation of the Poisson process, is the Cox process, where the intensity function is itself stochastic. We focus on Cox processes in which the intensity function is driven by a nite state space continuous-time Markov chain. We refer to these as Markov switching Cox processes (MSCP). We investigate some probabilistic properties of these processes, three new theorems for these processes are derived and we develop a Bayesian methodology to perform exact inference based on MCMC algorithms. Since the likelihood function is tractable, it facilitates the development of an exact methodology. Simulated studies are presented in order to investigate the efficiency of the methodology on the estimation of MSCP's intensity function and the parameters indexing its law. Finally, an analysis with real data is performed.
publishDate 2015
dc.date.none.fl_str_mv 2015-03-02
2019-08-11T02:06:53Z
2019-08-11T02:06:53Z
2025-09-09T00:50:39Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/1843/BUBD-9WGFNQ
url https://hdl.handle.net/1843/BUBD-9WGFNQ
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.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Minas Gerais
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
repository.name.fl_str_mv Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)
repository.mail.fl_str_mv repositorio@ufmg.br
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