Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical data
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2021 |
| Tipo de documento: | Artigo |
| Idioma: | por |
| Título da fonte: | Research, Society and Development |
| Texto Completo: | https://rsdjournal.org/index.php/rsd/article/view/11890 |
Resumo: | Statistical models serve to describe the probabilistic behavior of phenomena of interest, allowing them to be analyzed, predicted and made relevant decisions. Linear regression models are widely used in several areas. These models have strong assumptions such as independence between errors that in general do not fit spatial data, since these data allow dependence on the error covariance structure. Therefore, linear regression models can be compared with spatial models. Spatial data can be divided into 3 types: dot pattern, area data and geostatistical data. This work aims to evaluate linear regression models initially and later to compare them to spatial models for geostatistical data through the exponential covariance function. Unknown parameters are found in these models and the inference adopted in this work is Bayesian for allowing the expert's initial belief to be incorporated into the modeling, increasing the amount of information evaluated and therefore improving the estimates. When adjusting the models under simulated data sets, it is possible to verify the ability of the adjustments to recover the true values of the parameters and select the true model. This article is the result of an interest in analyzing the adjustment of the linear regression model with a set of artificial data with spatial dependence and comparing this to the adjustment of the spatial model, more specifically, based on geostatistical data. |
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Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical dataInferencia Bayesiana aplicada al modelo de regresión lineal y al modelo espacial: Un enfoque sobre la estructura de covarianza entre datos geoestadísticosInferência Bayesiana aplicada em modelo de regressão linear e modelo espacial: Uma abordagem sobre a estrutura de covariância entre os dados geoestatísticosSpatial StatisticsGeostatisticsBayesian inferenceMarkov chains Monte CarloDICLinear Regression ModelMean square error.Estadística espacialGeoestadísticaInferencia bayesianaModelo de regresión linealMétodos de Monte Carlo a través de cadenas de MarkovDICError cuadrático medio.Estatística EspacialGeoestatísticaInferência BayesianaModelo de Regressão LinearMétodos de Monte Carlo via cadeias de MarkovDICErro médio quadrático.Statistical models serve to describe the probabilistic behavior of phenomena of interest, allowing them to be analyzed, predicted and made relevant decisions. Linear regression models are widely used in several areas. These models have strong assumptions such as independence between errors that in general do not fit spatial data, since these data allow dependence on the error covariance structure. Therefore, linear regression models can be compared with spatial models. Spatial data can be divided into 3 types: dot pattern, area data and geostatistical data. This work aims to evaluate linear regression models initially and later to compare them to spatial models for geostatistical data through the exponential covariance function. Unknown parameters are found in these models and the inference adopted in this work is Bayesian for allowing the expert's initial belief to be incorporated into the modeling, increasing the amount of information evaluated and therefore improving the estimates. When adjusting the models under simulated data sets, it is possible to verify the ability of the adjustments to recover the true values of the parameters and select the true model. This article is the result of an interest in analyzing the adjustment of the linear regression model with a set of artificial data with spatial dependence and comparing this to the adjustment of the spatial model, more specifically, based on geostatistical data.Los modelos estadísticos sirven para describir el comportamiento probabilístico de los fenómenos de interés, permitiendo analizarlos, predecirlos y tomar decisiones relevantes. Los modelos de regresión lineal se utilizan ampliamente en varias áreas. Estos modelos tienen fuertes supuestos como la independencia entre errores que en general no se ajustan a los datos espaciales, ya que estos datos permiten la dependencia de la estructura de covarianza del error. Por lo tanto, los modelos de regresión lineal se pueden comparar con modelos espaciales. Los datos espaciales se pueden dividir en 3 tipos: patrón de puntos, datos de área y datos geoestadísticos. Este trabajo tiene como objetivo evaluar inicialmente los modelos de regresión lineal y posteriormente compararlos con modelos espaciales para datos geoestadísticos mediante la función de covarianza exponencial. En estos modelos se encuentran parámetros desconocidos y la inferencia adoptada en este trabajo es bayesiana para permitir que la creencia inicial del experto se incorpore al modelado, aumentando la cantidad de información evaluada y por tanto mejorando las estimaciones. Al ajustar los modelos bajo conjuntos de datos simulados, es posible verificar la capacidad de los ajustes para recuperar los valores reales de los parámetros y seleccionar el modelo verdadero. Este artículo es el resultado de un interés en analizar el ajuste del modelo de regresión lineal con un conjunto de datos artificiales con dependencia espacial y compararlo con el ajuste del modelo espacial, más específicamente, basado en datos geoestadísticos.Modelos estatísticos servem para descrever o comportamento probabilístico de fenômenos de interesse permitindo analisá-los, prevê-los e tomar decisões pertinentes. Modelos de regressão linear são muito utilizados em diversas áreas. Esses modelos possuem suposições fortes como independência entre os erros que em geral não se ajustam a dados espaciais, já que estes dados permitem que haja dependência na estrutura de covariância dos erros. Portanto, modelos de regressão linear podem ser comparados com modelos espaciais. Dados espaciais podem ser divididos em 3 tipos: padrão de pontos, dados de área e dados geoestatísticos. Esse trabalho visa avaliar modelos de regressão linear inicialmente e posteriormente compará-los aos modelos espaciais para dados geoestatísticos através da função de covariância exponencial. Parâmetros desconhecidos são encontrados nesses modelos e a inferência adotada nesse trabalho é a Bayesiana por permitir que a crença inicial do especialista seja incorporada a modelagem, aumentando a quantidade de informação avaliada e melhorando portanto as estimativas. Ao ajustar os modelos sob conjuntos de dados simulados é possível verificar a capacidade dos ajustes recuperarem os verdadeiros valores dos parâmetros e selecionar o verdadeiro modelo. O presente artigo é resultado do interesse em analisar o ajuste do modelo de regressão linear com conjunto de dados artificiais com dependência espacial e comparar esse ao ajuste do modelo espacial, mais especificamente, a partir de dados geoestatísticos.Research, Society and Development2021-01-14info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://rsdjournal.org/index.php/rsd/article/view/1189010.33448/rsd-v10i1.11890Research, Society and Development; Vol. 10 No. 1; e31910111890Research, Society and Development; Vol. 10 Núm. 1; e31910111890Research, Society and Development; v. 10 n. 1; e319101118902525-3409reponame:Research, Society and Developmentinstname:Universidade Federal de Itajubá (UNIFEI)instacron:UNIFEIporhttps://rsdjournal.org/index.php/rsd/article/view/11890/10530Copyright (c) 2021 Rondinelli Gomes Bragançahttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessBragança, Rondinelli Gomes2021-02-20T21:19:23Zoai:ojs.pkp.sfu.ca:article/11890Revistahttps://rsdjournal.org/index.php/rsd/indexPUBhttps://rsdjournal.org/index.php/rsd/oairsd.articles@gmail.com2525-34092525-3409opendoar:2024-01-17T09:33:36.309708Research, Society and Development - Universidade Federal de Itajubá (UNIFEI)false |
| dc.title.none.fl_str_mv |
Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical data Inferencia Bayesiana aplicada al modelo de regresión lineal y al modelo espacial: Un enfoque sobre la estructura de covarianza entre datos geoestadísticos Inferência Bayesiana aplicada em modelo de regressão linear e modelo espacial: Uma abordagem sobre a estrutura de covariância entre os dados geoestatísticos |
| title |
Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical data |
| spellingShingle |
Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical data Bragança, Rondinelli Gomes Spatial Statistics Geostatistics Bayesian inference Markov chains Monte Carlo DIC Linear Regression Model Mean square error. Estadística espacial Geoestadística Inferencia bayesiana Modelo de regresión lineal Métodos de Monte Carlo a través de cadenas de Markov DIC Error cuadrático medio. Estatística Espacial Geoestatística Inferência Bayesiana Modelo de Regressão Linear Métodos de Monte Carlo via cadeias de Markov DIC Erro médio quadrático. |
| title_short |
Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical data |
| title_full |
Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical data |
| title_fullStr |
Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical data |
| title_full_unstemmed |
Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical data |
| title_sort |
Bayesian inference applied to linear regression model and spatial model: An approach on the covariance structure between geostatistical data |
| author |
Bragança, Rondinelli Gomes |
| author_facet |
Bragança, Rondinelli Gomes |
| author_role |
author |
| dc.contributor.author.fl_str_mv |
Bragança, Rondinelli Gomes |
| dc.subject.por.fl_str_mv |
Spatial Statistics Geostatistics Bayesian inference Markov chains Monte Carlo DIC Linear Regression Model Mean square error. Estadística espacial Geoestadística Inferencia bayesiana Modelo de regresión lineal Métodos de Monte Carlo a través de cadenas de Markov DIC Error cuadrático medio. Estatística Espacial Geoestatística Inferência Bayesiana Modelo de Regressão Linear Métodos de Monte Carlo via cadeias de Markov DIC Erro médio quadrático. |
| topic |
Spatial Statistics Geostatistics Bayesian inference Markov chains Monte Carlo DIC Linear Regression Model Mean square error. Estadística espacial Geoestadística Inferencia bayesiana Modelo de regresión lineal Métodos de Monte Carlo a través de cadenas de Markov DIC Error cuadrático medio. Estatística Espacial Geoestatística Inferência Bayesiana Modelo de Regressão Linear Métodos de Monte Carlo via cadeias de Markov DIC Erro médio quadrático. |
| description |
Statistical models serve to describe the probabilistic behavior of phenomena of interest, allowing them to be analyzed, predicted and made relevant decisions. Linear regression models are widely used in several areas. These models have strong assumptions such as independence between errors that in general do not fit spatial data, since these data allow dependence on the error covariance structure. Therefore, linear regression models can be compared with spatial models. Spatial data can be divided into 3 types: dot pattern, area data and geostatistical data. This work aims to evaluate linear regression models initially and later to compare them to spatial models for geostatistical data through the exponential covariance function. Unknown parameters are found in these models and the inference adopted in this work is Bayesian for allowing the expert's initial belief to be incorporated into the modeling, increasing the amount of information evaluated and therefore improving the estimates. When adjusting the models under simulated data sets, it is possible to verify the ability of the adjustments to recover the true values of the parameters and select the true model. This article is the result of an interest in analyzing the adjustment of the linear regression model with a set of artificial data with spatial dependence and comparing this to the adjustment of the spatial model, more specifically, based on geostatistical data. |
| publishDate |
2021 |
| dc.date.none.fl_str_mv |
2021-01-14 |
| dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.uri.fl_str_mv |
https://rsdjournal.org/index.php/rsd/article/view/11890 10.33448/rsd-v10i1.11890 |
| url |
https://rsdjournal.org/index.php/rsd/article/view/11890 |
| identifier_str_mv |
10.33448/rsd-v10i1.11890 |
| dc.language.iso.fl_str_mv |
por |
| language |
por |
| dc.relation.none.fl_str_mv |
https://rsdjournal.org/index.php/rsd/article/view/11890/10530 |
| dc.rights.driver.fl_str_mv |
Copyright (c) 2021 Rondinelli Gomes Bragança https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
Copyright (c) 2021 Rondinelli Gomes Bragança https://creativecommons.org/licenses/by/4.0 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
Research, Society and Development |
| publisher.none.fl_str_mv |
Research, Society and Development |
| dc.source.none.fl_str_mv |
Research, Society and Development; Vol. 10 No. 1; e31910111890 Research, Society and Development; Vol. 10 Núm. 1; e31910111890 Research, Society and Development; v. 10 n. 1; e31910111890 2525-3409 reponame:Research, Society and Development instname:Universidade Federal de Itajubá (UNIFEI) instacron:UNIFEI |
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Universidade Federal de Itajubá (UNIFEI) |
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UNIFEI |
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UNIFEI |
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Research, Society and Development |
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Research, Society and Development |
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Research, Society and Development - Universidade Federal de Itajubá (UNIFEI) |
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rsd.articles@gmail.com |
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1797052668598812672 |