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Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes
Statistical modeling of temporal point patterns is an important problem in several areas. The Cox process, a Poisson process where the intensity function is stochastic, is a common model for such data. We present a new class of unidimensional Cox process models in which the intensity function assume...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8733934/ https://www.ncbi.nlm.nih.gov/pubmed/35013655 http://dx.doi.org/10.1007/s11222-021-10074-y |
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author | Gonçalves, Flávio B. Dutra, Lívia M. Silva, Roger W. C. |
author_facet | Gonçalves, Flávio B. Dutra, Lívia M. Silva, Roger W. C. |
author_sort | Gonçalves, Flávio B. |
collection | PubMed |
description | Statistical modeling of temporal point patterns is an important problem in several areas. The Cox process, a Poisson process where the intensity function is stochastic, is a common model for such data. We present a new class of unidimensional Cox process models in which the intensity function assumes parametric functional forms that switch according to a continuous-time Markov chain. A novel methodology is introduced to perform exact (up to Monte Carlo error) Bayesian inference based on MCMC algorithms. The reliability of the algorithms depends on a variety of specifications which are carefully addressed, resulting in a computationally efficient (in terms of computing time) algorithm and enabling its use with large data sets. Simulated and real examples are presented to illustrate the efficiency and applicability of the methodology. A specific model to fit epidemic curves is proposed and used to analyze data from Dengue Fever in Brazil and COVID-19 in some countries. |
format | Online Article Text |
id | pubmed-8733934 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-87339342022-01-06 Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes Gonçalves, Flávio B. Dutra, Lívia M. Silva, Roger W. C. Stat Comput Article Statistical modeling of temporal point patterns is an important problem in several areas. The Cox process, a Poisson process where the intensity function is stochastic, is a common model for such data. We present a new class of unidimensional Cox process models in which the intensity function assumes parametric functional forms that switch according to a continuous-time Markov chain. A novel methodology is introduced to perform exact (up to Monte Carlo error) Bayesian inference based on MCMC algorithms. The reliability of the algorithms depends on a variety of specifications which are carefully addressed, resulting in a computationally efficient (in terms of computing time) algorithm and enabling its use with large data sets. Simulated and real examples are presented to illustrate the efficiency and applicability of the methodology. A specific model to fit epidemic curves is proposed and used to analyze data from Dengue Fever in Brazil and COVID-19 in some countries. Springer US 2022-01-06 2022 /pmc/articles/PMC8733934/ /pubmed/35013655 http://dx.doi.org/10.1007/s11222-021-10074-y Text en © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Gonçalves, Flávio B. Dutra, Lívia M. Silva, Roger W. C. Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes |
title | Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes |
title_full | Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes |
title_fullStr | Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes |
title_full_unstemmed | Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes |
title_short | Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes |
title_sort | exact and computationally efficient bayesian inference for generalized markov modulated poisson processes |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8733934/ https://www.ncbi.nlm.nih.gov/pubmed/35013655 http://dx.doi.org/10.1007/s11222-021-10074-y |
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