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dc.rights.licenseAtribución-NoComercial 4.0 Internacional
dc.contributor.advisorPericchi Guerra, Luis Raul
dc.contributor.advisorSalazar Uribe, Juan Carlos
dc.contributor.authorCorreal Álvarez, Cristian David
dc.date.accessioned2020-06-24T21:58:41Z
dc.date.available2020-06-24T21:58:41Z
dc.date.issued2020-06-23
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/77686
dc.description.abstractLas distribuciones a priori son indispensables en estadística bayesiana para hacer inferencia, porque reflejan el conocimiento previo de un parámetro desconocido; estas distribuciones han sido utilizadas en diferentes áreas con el fin de mejorar las inferencias de los modelos planeados. Por lo anterior, en este trabajo se consideran distribuciones a priori en tres situaciones de interés. En la primera situación, se propone una metodología para combinar distribuciones a priori considerando el estimador de James-Stein; pero con varianza no constante por experto como una forma de penalizar el conocimiento de éste. Se muestra que la metodología es razonable para seleccionar la distribución a priori de interés ya que considera a todos los expertos del estudio y no se descarta información. En la segunda situación, se utilizan distribuciones a priori beta para modelar la fracción de defectos p en planes de aceptación por atributo; el procedimiento es válido para frecuentistas y bayesianos a la hora de determinar el tamaño óptimo de la muestra y decidir la aceptabilidad de un lote enviado a inspeccionar. Se presenta un procedimiento para minimizar una suma ponderada de los riesgos clásicos y esperados del productor y consumidor, y se muestra que la inclusión de funciones de peso/densidad para la fracción de defectos puede disminuir significativamente la cantidad de pruebas requeridas; sin embargo, su principal ventaja no es necesariamente la reducción del tamaño de la muestra, sino una mejor evaluación del riesgo real del tomador de decisiones. En la tercera situación, se modelan los aciertos obtenidos de dos encuestas aplicadas a estudiantes universitarios a lo largo del semestre académico 2018-1, con un modelo logístico multinivel utilizando las distribuciones a priori beta 2 escalada y gamma-inversa, para modelar el efecto aleatorio. Los resultados se comparan con modelos tradicionales donde no se considera el efecto aleatorio dentro de cada grupo. Se concluye que los modelos de efecto aleatorio tienen mayor capacidad predictiva de los datos y presentan intervalos de probabilidad más precisos que los modelos de efecto fijo.
dc.description.abstractPrior distributions are indispensable in Bayesian statistics to make inference because they reflect prior knowledge of an unknown parameter; these distributions have been used in different areas in order to improve the inferences of the planned models. In the first situation, prior distributions are considered for three problems of interest. Initially a methodology is proposed to combine a prior distributions considering the James-Stein method; but with variance not constant by expert as a way to penalize expert knowledge. It is shown that the methodology is reasonable to select the a prior distribution of interest since it considers all the experts in the study and does not discard information. In the second situation, a prior beta distributions are used to model the fraction $p$ of defects in acceptance plans by attribute; the procedure is valid for frequentists and Bayesians when determining the optimal sample size and deciding the acceptability of a lot sent to inspect. A procedure is presented to minimize a weighted sum of the classic risks and expected risks of the producer and consumer, it is shown that the inclusion of weight/density functions for the defect fraction can significantly decrease the amount of tests required. However, its main advantage is not necessarily the reduction of the sample size, but a better evaluation of the real risk of the decision maker. In the third situation, the successes obtained from two surveys applied to university students throughout the 2018-1 academic semester are modeled, with a multilevel logistic model using the scaled beta 2 and inverse-gamma prior distributions, to model the random effects. The results are compared with traditional models where the random effect within each group is not considered. It is concluded that the random effect models have a greater predictive capacity of the data and present less wide probability intervals than the fixed effect models.
dc.format.extent96
dc.format.mimetypeapplication/pdf
dc.language.isospa
dc.rightsDerechos reservados - Universidad Nacional de Colombia
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/
dc.subject.ddc510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
dc.titleMétodos para la selección de distribuciones a priori utilizando el estimador de James-Stein, planes de muestreo por atributo y modelos logísticos multinivel
dc.title.alternativeMethods for prior distributions selections using the James-Stein estimator, attribute sampling plans and multilevel logistics models
dc.typeOtro
dc.rights.spaAcceso abierto
dc.type.driverinfo:eu-repo/semantics/other
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.publisher.programMedellín - Ciencias - Doctorado en Ciencias - Estadística
dc.contributor.corporatenameUniversidad Nacional de Colombia - Sede Medellín
dc.description.degreelevelDoctorado
dc.publisher.departmentEscuela de estadística
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellín
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.subject.proposalBayesian inference
dc.subject.proposalInferencia bayesiana
dc.subject.proposalDistribuciones a priori
dc.subject.proposalPrior distributions
dc.subject.proposalPlanes de muestreo por atributo
dc.subject.proposalSampling plans by attribute
dc.subject.proposalProducer and consumer risk
dc.subject.proposalRiesgo del productor y consumidor
dc.subject.proposalBayesian logistic models
dc.subject.proposalModelos logísticos bayesianos
dc.subject.proposalCombinación de distribuciones a priori
dc.subject.proposalCombination of a prior distributions
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