Semiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspective

ilustraciones, gráficas, tablas

Autores:: Zárate Solano, Héctor Manuel

Tipo de recurso:: Doctoral thesis

Fecha de publicación:: 2022

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: eng

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dc.title.eng.fl_str_mv	Semiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspective
dc.title.translated.spa.fl_str_mv	Suavizamiento spline semiparamétrico para modelar simultaneamente las funciones media y varianza con respuestas de la familia exponencial biparamétrica: una perspectiva bayesiana
title	Semiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspective
spellingShingle	Semiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspective 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Spline theory Bayesian statistical decision theory Lineal models (statistics) Teoría Spline Teoría bayesiana de decisiones estadísticas Modelos lineales (Estadística) Semiparametric heteroscedastic models Calculus of variations Optimization Biparametric exponential models Markov chain Monte Carlo Generalized linear models Smoothing spline Asymmetric distributions Variational bayesian learning Modelos semiparamétricos Familia exponencial biparamétrica Cadenas de markov Monte Carlo Modelos lineales generalizados Suavizamiento spline Distribuciones asimétricas Aprendizaje bayesiano variacional Análisis numérico Numerical analysis
title_short	Semiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspective
title_full	Semiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspective
title_fullStr	Semiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspective
title_full_unstemmed	Semiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspective
title_sort	Semiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspective
dc.creator.fl_str_mv	Zárate Solano, Héctor Manuel
dc.contributor.advisor.spa.fl_str_mv	Cepeda Cuervo, Edilberto
dc.contributor.author.spa.fl_str_mv	Zárate Solano, Héctor Manuel
dc.contributor.researchgroup.spa.fl_str_mv	Inferencia Bayesiana
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
topic	510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Spline theory Bayesian statistical decision theory Lineal models (statistics) Teoría Spline Teoría bayesiana de decisiones estadísticas Modelos lineales (Estadística) Semiparametric heteroscedastic models Calculus of variations Optimization Biparametric exponential models Markov chain Monte Carlo Generalized linear models Smoothing spline Asymmetric distributions Variational bayesian learning Modelos semiparamétricos Familia exponencial biparamétrica Cadenas de markov Monte Carlo Modelos lineales generalizados Suavizamiento spline Distribuciones asimétricas Aprendizaje bayesiano variacional Análisis numérico Numerical analysis
dc.subject.lemb.eng.fl_str_mv	Spline theory Bayesian statistical decision theory Lineal models (statistics)
dc.subject.lemb.spa.fl_str_mv	Teoría Spline Teoría bayesiana de decisiones estadísticas Modelos lineales (Estadística)
dc.subject.proposal.eng.fl_str_mv	Semiparametric heteroscedastic models Calculus of variations Optimization Biparametric exponential models Markov chain Monte Carlo Generalized linear models Smoothing spline Asymmetric distributions Variational bayesian learning
dc.subject.proposal.spa.fl_str_mv	Modelos semiparamétricos Familia exponencial biparamétrica Cadenas de markov Monte Carlo Modelos lineales generalizados Suavizamiento spline Distribuciones asimétricas Aprendizaje bayesiano variacional
dc.subject.unesco.spa.fl_str_mv	Análisis numérico
dc.subject.unesco.eng.fl_str_mv	Numerical analysis
description	ilustraciones, gráficas, tablas
publishDate	2022
dc.date.accessioned.none.fl_str_mv	2022-02-05T00:31:26Z
dc.date.available.none.fl_str_mv	2022-02-05T00:31:26Z
dc.date.issued.none.fl_str_mv	2022-01
dc.type.spa.fl_str_mv	Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/doctoralThesis
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dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/80887
dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.unal.edu.co/
url	https://repositorio.unal.edu.co/handle/unal/80887 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv	eng
language	eng
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Bayesian analysis for penalized spline regression using winbugs. Journal of Statistical Software, 14:1–24, 2005. Crevar, M. Shared file systems: Determining the best choice for your distributed SAS® foundation applications. SAS Institute Inc., Cary, NC., pages 1–11, 2017. 21 Dey, D.K., Gelfand, A.E., and Peng, F. Overdispersed generalized linear models. Journal of Statistical Planning and Inference,, 64(64):93–108, 1997. Evans, M. J. and Rosenthal, J. S. Probability and Statistics: The science of Uncertainty. The American Statistician. New York: W.H Freeman and Company, 2004. Gilks, W.R., Richardson, S., and Spiegelhalter, D.J. Markov Chain Monte Carlo in practice. Interdisciplinary Statistics. Chapman Hall/CR, 1998. Green, P.J. and Silverman, B.W. Nonparametric Regression and Generalized Linear Models: A roughness penalty approach. Chapman and Hall, London, 1994. Groll, A., Hambuckers, J., , Kneib, T., and Umlauf, N. 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Statistics, Optimization Information Computing, 9(2):351–367, 2021.
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dc.format.extent.spa.fl_str_mv	xvii, 133 páginas
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Bogotá - Ciencias - Doctorado en Ciencias - Estadística
dc.publisher.department.spa.fl_str_mv	Departamento de Estadística
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv	Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Bogotá
institution	Universidad Nacional de Colombia
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spelling	Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cepeda Cuervo, Edilberto5d0ed32887a693c303b0ad910550b643600Zárate Solano, Héctor Manuela949726249a602be2f603c3cd9aa37a2Inferencia Bayesiana2022-02-05T00:31:26Z2022-02-05T00:31:26Z2022-01https://repositorio.unal.edu.co/handle/unal/80887Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, gráficas, tablasStatistical applications need to address an increasing complexity due to new data arising from recent technologies, new phenomenons, and diverse sources of uncertainty. The demand for flexible methods with non-standard data structures, high-dimensional real-time estimation, and latent models framework have caused semiparametric modeling to play a crucial role in contemporary statistical analysis. We provide flexible Bayesian methods to jointly infer the mean, variance, and skewness functions when the response variable comes either from a two-parameter exponential family or asymmetric distributions. Hence, we implemented Bayesian algorithms based on MCMC sampling techniques and deterministic variational Bayesian learning theory. In these settings, each sub-model depends on some covariates parametrically and for others in a non-parametrically way. It follows that understanding how the moments change with predictors is a goal of Statistics, and it is of intrinsic interest given the role in approximating other quantities. We propose several modeling scenarios that benefit from the fusion of the graphical models' approach to Bayesian semiparametric regression under the architecture of GLM models. The significance and implications of our strategy lie in its potential to contribute to a unified computational methodology that provides insight into many complex models that otherwise could be intractable analytically. Therefore, combining data models and algorithms contribute to solving real-world problems enjoying crucial advantages related to faster computation time, which allow not only to explore quickly many models for the data but to estimate them accurately.Las aplicaciones estadísticas deben abordar una complejidad cada vez mayor debido a los nuevos datos que surgen con las tecnologías recientes, los nuevos fenómenos y las diversas fuentes de incertidumbre. La demanda por métodos con estructuras de datos no estándar, estimación en tiempo real de alta dimensión y modelos latentes adecuados ha causado que los modelos semiparamétricos desempeñen un papel crucial en el análisis estadístico reciente. En esta tesis se implementan métodos Bayesianos flexibles para inferir conjuntamente las funciones de media, varianza y asimetría cuando la variable de respuesta proviene de la familia exponencial biparamétrica o de distribuciones asimétricas. La aproximación es obtenida con métodos basados en técnicas de simulación de Monte Carlo con cadenas de markov y en algoritmos de aprendizaje variacional determinístico. En estos escenarios, cada submodelo incluye variables en forma paramétrica y no paramétrica para analizar el efecto de los predictores sobre los momentos. Los escenarios de modelamiento se benefician de la fusión entre los modelos gráficos y la regresión semiparamétrica Bayesiana utilizando la arquitectura de modelos lineales generalizados. La importancia e implicaciones de nuestra estrategia radican en su potencial para contribuir con una metodología computacional unificada que proporciona información sobre una gran variedad de modelos complejos que, de otro modo, podrían resultar analíticamente intratables. Por lo tanto, la combinación de modelos de datos y algoritmos contribuye a resolver problemas del mundo real y disfruta de ventajas cruciales relacionadas con el bajo tiempo de cómputo, lo cual permite no solo explorar rápidamente muchos modelos para los datos, sino también estimarlos con precisión. (Texto tomado de la fuente).Incluye anexosDoctoradoDoctor en Ciencias - Estadísticaxvii, 133 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Doctorado en Ciencias - EstadísticaDepartamento de EstadísticaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasSpline theoryBayesian statistical decision theoryLineal models (statistics)Teoría SplineTeoría bayesiana de decisiones estadísticasModelos lineales (Estadística)Semiparametric heteroscedastic modelsCalculus of variationsOptimizationBiparametric exponential modelsMarkov chain Monte CarloGeneralized linear modelsSmoothing splineAsymmetric distributionsVariational bayesian learningModelos semiparamétricosFamilia exponencial biparamétricaCadenas de markov Monte CarloModelos lineales generalizadosSuavizamiento splineDistribuciones asimétricasAprendizaje bayesiano variacionalAnálisis numéricoNumerical analysisSemiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspectiveSuavizamiento spline semiparamétrico para modelar simultaneamente las funciones media y varianza con respuestas de la familia exponencial biparamétrica: una perspectiva bayesianaTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDAnderson, D. F. and Livingston, P. S. The zero-divisor graph of a commutative ring. Journal of Algebra, 217(2):434–447, 1999.Berry, S., Carroll, R., and Ruppert, D. Bayesian smoothing and regression splines for measurement error problems. Journal of the American Statistical Association, 97(457):160 – 169, 2002.Bishop, C. M. Pattern recognition and Machine Learning, volume 1 of Graduate Texts in Mathematics. New York : Springer, 2006.Blei, D. M., Kucukelbir, A., and McAuliffe, J.D. Variational inference: a review for statisticians. Journal of the American Statistical Association, 112:859–857, 2017.Brooks, S., Gelman, A., Jones, G., and Meng, X. Handbook of Markov Chain Monte Carlo. Handbooks of Modern and Statistical Methods. Chapman Hall/CR, 2011.Cepeda, E. and Gamerman, D. Bayesian modeling of variance heterogeneity in normal regression models. J. Prob. Stat, 14:207–221, 2001.Crainiceanu, C., Ruppert, D., and Wand, M. Bayesian analysis for penalized spline regression using winbugs. Journal of Statistical Software, 14:1–24, 2005.Crevar, M. Shared file systems: Determining the best choice for your distributed SAS® foundation applications. SAS Institute Inc., Cary, NC., pages 1–11, 2017. 21Dey, D.K., Gelfand, A.E., and Peng, F. Overdispersed generalized linear models. Journal of Statistical Planning and Inference,, 64(64):93–108, 1997.Evans, M. J. and Rosenthal, J. S. Probability and Statistics: The science of Uncertainty. The American Statistician. New York: W.H Freeman and Company, 2004.Gilks, W.R., Richardson, S., and Spiegelhalter, D.J. Markov Chain Monte Carlo in practice. Interdisciplinary Statistics. Chapman Hall/CR, 1998.Green, P.J. and Silverman, B.W. Nonparametric Regression and Generalized Linear Models: A roughness penalty approach. Chapman and Hall, London, 1994.Groll, A., Hambuckers, J., , Kneib, T., and Umlauf, N. Lasso-type penalization in the framework of generalized additive models for location, scale and shape. 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Statistics, Optimization Information Computing, 9(2):351–367, 2021.Público generalORIGINAL7219498.2021.pdf7219498.2021.pdfTesis de Doctorado en Ciencias - Estadísticaapplication/pdf4756185https://repositorio.unal.edu.co/bitstream/unal/80887/4/7219498.2021.pdf065e4358dbfb8a106fa9ec981cf4ac2bMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-84074https://repositorio.unal.edu.co/bitstream/unal/80887/5/license.txt8153f7789df02f0a4c9e079953658ab2MD55THUMBNAIL7219498.2021.pdf.jpg7219498.2021.pdf.jpgGenerated Thumbnailimage/jpeg4922https://repositorio.unal.edu.co/bitstream/unal/80887/6/7219498.2021.pdf.jpg302590e62151297d196efed118852031MD56unal/80887oai:repositorio.unal.edu.co:unal/808872023-07-31 23:04:25.228Repositorio Institucional Universidad Nacional de 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EVESURBIFBPUiBMQSBTRUNSRVRBUsONQSBHRU5FUkFMLiAqTEEgVEVTSVMgQSBQVUJMSUNBUiBERUJFIFNFUiBMQSBWRVJTScOTTiBGSU5BTCBBUFJPQkFEQS4gCgpBbCBoYWNlciBjbGljIGVuIGVsIHNpZ3VpZW50ZSBib3TDs24sIHVzdGVkIGluZGljYSBxdWUgZXN0w6EgZGUgYWN1ZXJkbyBjb24gZXN0b3MgdMOpcm1pbm9zLiBTaSB0aWVuZSBhbGd1bmEgZHVkYSBzb2JyZSBsYSBsaWNlbmNpYSwgcG9yIGZhdm9yLCBjb250YWN0ZSBjb24gZWwgYWRtaW5pc3RyYWRvciBkZWwgc2lzdGVtYS4KClVOSVZFUlNJREFEIE5BQ0lPTkFMIERFIENPTE9NQklBIC0gw5psdGltYSBtb2RpZmljYWNpw7NuIDE5LzEwLzIwMjEK

Semiparametric smoothing spline to joint mean and variance models with responses from the biparametric exponential family: a bayesian perspective

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