Likelihood Function through the Delta Approximation in Mixed SDE models
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/31286 https://doi.org/Jamba, N.T.; Jacinto, G.; Filipe, P.A.; Braumann, C.A. Likelihood Function through the Delta Approximation in Mixed SDE Models. Mathematics 2022, 10, 385. https://doi.org/10.3390/math10030385 https://doi.org/10.3390/math10030385 |
Resumo: | Stochastic differential equations (SDE) appropriately describe a variety of phenomena occurring in random environments, such as the growth dynamics of individual animals. Using appropriate weight transformations and a variant of the Ornstein–Uhlenbeck model, one obtains a general model for the evolution of cattle weight. The model parameters are \alpha, the average transformed weight at maturity, \beta, a growth parameter, and \sigmas, a measure of environmental fluctuations intensity. We briefly review our previous work on estimation and prediction issues for this model and some generalizations, considering fixed parameters. In order to incorporate individual characteristics of the animals, we now consider that the parameters \alpha and \beta are Gaussian random variables varying from animal to animal, which results in SDE mixed models. We estimate parameters by maximum likelihood, but, since a closed-form expression for the likelihood function is usually not possible, we approximate it using our proposed delta approximation method. Using simulated data, we estimate the model parameters and compare them with existing methodologies, showing that the proposed method is a good alternative. It also overcomes the existing methodologies requirement of having all animals weighed at the same ages; thus, we apply it to real data, where such a requirement fails. |
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Likelihood Function through the Delta Approximation in Mixed SDE modelsdelta approximationmaximum likelihood estimation methodmixed modelsstochastic differential equationsStochastic differential equations (SDE) appropriately describe a variety of phenomena occurring in random environments, such as the growth dynamics of individual animals. Using appropriate weight transformations and a variant of the Ornstein–Uhlenbeck model, one obtains a general model for the evolution of cattle weight. The model parameters are \alpha, the average transformed weight at maturity, \beta, a growth parameter, and \sigmas, a measure of environmental fluctuations intensity. We briefly review our previous work on estimation and prediction issues for this model and some generalizations, considering fixed parameters. In order to incorporate individual characteristics of the animals, we now consider that the parameters \alpha and \beta are Gaussian random variables varying from animal to animal, which results in SDE mixed models. We estimate parameters by maximum likelihood, but, since a closed-form expression for the likelihood function is usually not possible, we approximate it using our proposed delta approximation method. Using simulated data, we estimate the model parameters and compare them with existing methodologies, showing that the proposed method is a good alternative. It also overcomes the existing methodologies requirement of having all animals weighed at the same ages; thus, we apply it to real data, where such a requirement fails.FCT (Fundação para a Ciência e a Tecnologia, Portugal), project UID/04674/2020 (CIMA). PDR2020-1.0.1-FEADER-031130-Go BovMais-Productivity improvement in the system of bovine raising for meat, PDR 2020 (European Agricultural Fund for Rural Development).MDPI2022-03-09T11:44:27Z2022-03-092022-01-27T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/31286https://doi.org/Jamba, N.T.; Jacinto, G.; Filipe, P.A.; Braumann, C.A. Likelihood Function through the Delta Approximation in Mixed SDE Models. Mathematics 2022, 10, 385. https://doi.org/10.3390/math10030385http://hdl.handle.net/10174/31286https://doi.org/10.3390/math10030385eng2227-7390https://www.mdpi.com/2227-7390/10/3/385MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científicad39830@alunos.uevora.ptgjcj@uevora.ptpatricia.filipe@iscte-iul.ptbraumann@uevora.pt336Jamba, Nelson T.Jacinto, GonçaloFilipe, Patrícia A.Braumann, Carlos A.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T19:30:14Zoai:dspace.uevora.pt:10174/31286Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:20:19.875332Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Likelihood Function through the Delta Approximation in Mixed SDE models |
title |
Likelihood Function through the Delta Approximation in Mixed SDE models |
spellingShingle |
Likelihood Function through the Delta Approximation in Mixed SDE models Jamba, Nelson T. delta approximation maximum likelihood estimation method mixed models stochastic differential equations |
title_short |
Likelihood Function through the Delta Approximation in Mixed SDE models |
title_full |
Likelihood Function through the Delta Approximation in Mixed SDE models |
title_fullStr |
Likelihood Function through the Delta Approximation in Mixed SDE models |
title_full_unstemmed |
Likelihood Function through the Delta Approximation in Mixed SDE models |
title_sort |
Likelihood Function through the Delta Approximation in Mixed SDE models |
author |
Jamba, Nelson T. |
author_facet |
Jamba, Nelson T. Jacinto, Gonçalo Filipe, Patrícia A. Braumann, Carlos A. |
author_role |
author |
author2 |
Jacinto, Gonçalo Filipe, Patrícia A. Braumann, Carlos A. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Jamba, Nelson T. Jacinto, Gonçalo Filipe, Patrícia A. Braumann, Carlos A. |
dc.subject.por.fl_str_mv |
delta approximation maximum likelihood estimation method mixed models stochastic differential equations |
topic |
delta approximation maximum likelihood estimation method mixed models stochastic differential equations |
description |
Stochastic differential equations (SDE) appropriately describe a variety of phenomena occurring in random environments, such as the growth dynamics of individual animals. Using appropriate weight transformations and a variant of the Ornstein–Uhlenbeck model, one obtains a general model for the evolution of cattle weight. The model parameters are \alpha, the average transformed weight at maturity, \beta, a growth parameter, and \sigmas, a measure of environmental fluctuations intensity. We briefly review our previous work on estimation and prediction issues for this model and some generalizations, considering fixed parameters. In order to incorporate individual characteristics of the animals, we now consider that the parameters \alpha and \beta are Gaussian random variables varying from animal to animal, which results in SDE mixed models. We estimate parameters by maximum likelihood, but, since a closed-form expression for the likelihood function is usually not possible, we approximate it using our proposed delta approximation method. Using simulated data, we estimate the model parameters and compare them with existing methodologies, showing that the proposed method is a good alternative. It also overcomes the existing methodologies requirement of having all animals weighed at the same ages; thus, we apply it to real data, where such a requirement fails. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-03-09T11:44:27Z 2022-03-09 2022-01-27T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10174/31286 https://doi.org/Jamba, N.T.; Jacinto, G.; Filipe, P.A.; Braumann, C.A. Likelihood Function through the Delta Approximation in Mixed SDE Models. Mathematics 2022, 10, 385. https://doi.org/10.3390/math10030385 http://hdl.handle.net/10174/31286 https://doi.org/10.3390/math10030385 |
url |
http://hdl.handle.net/10174/31286 https://doi.org/Jamba, N.T.; Jacinto, G.; Filipe, P.A.; Braumann, C.A. Likelihood Function through the Delta Approximation in Mixed SDE Models. Mathematics 2022, 10, 385. https://doi.org/10.3390/math10030385 https://doi.org/10.3390/math10030385 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2227-7390 https://www.mdpi.com/2227-7390/10/3/385 MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica d39830@alunos.uevora.pt gjcj@uevora.pt patricia.filipe@iscte-iul.pt braumann@uevora.pt 336 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
MDPI |
publisher.none.fl_str_mv |
MDPI |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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