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What is the effect of sample and prior distributions on a Bayesian autoregressive linear model? An application to piped water consumption

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dc.contributor.authorRamírez Hassan, Andrés
dc.contributor.authorCardona Jiménez, Jhonatan
dc.contributor.authorPericchi Guerra, Raul
dc.coverage.spatialMedellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degreeseng
dc.creator.emailaramir21@eafit.edu.co
dc.creator.emailjcardonj@dme.ufrj.br
dc.creator.emaillrpericchi@uprrp.edu
dc.date.accessioned2014-08-01T20:58:17Z
dc.date.available2014-08-01T20:58:17Z
dc.date.issued2014-07-23
dc.description.abstractIn this paper we analyze the effect of four possible alternatives regarding the prior distributions in a linear model with autoregressive errors to predict piped water consumption: Normal-Gamma, Normal-Scaled Beta two, Studentized-Gamma and Student's t-Scaled Beta two. We show the effects of these prior distributions on the posterior distributions under different assumptions associated with the coefficient of variation of prior hyperparameters in a context where there is a conflict between the sample information and the elicited hyperparameters. We show that the posterior parameters are less affected by the prior hyperparameters when the Studentized-Gamma and Student's t-Scaled Beta two models are used. We show that the Normal-Gamma model obtains sensible outcomes in predictions when there is a small sample size. However, this property is lost when the experts overestimate the certainty of their knowledge. In the case that the experts greatly trust their beliefs, it is a good idea to use Student's t distribution as the prior distribution, because we obtain small posterior predictive errors. In addition, we find that the posterior predictive distributions using one of the versions of Student's t as prior are robust to the coefficient of variation of the prior parameters. Finally, it is shown that the Normal-Gamma model has a posterior distribution of the variance concentrated near zero when there is a high level of confidence in the experts' knowledge: this implies a narrow posterior predictive credibility interval, especially using small sample sizes.eng
dc.format.mimetypeapplication/pdf
dc.identifier.instnameinstname:Universidad EAFIT
dc.identifier.jelC11
dc.identifier.jelC53
dc.identifier.reponamereponame:Repositorio Institucional Universidad EAFIT
dc.identifier.repourlrepourl:https://repository.eafit.edu.co
dc.identifier.urihttps://hdl.handle.net/10784/2857
dc.language.isoeng
dc.publisherUniversidad EAFITspa
dc.publisher.departmentCentro Valor Públicospa
dc.publisher.facultyEscuela de Economía y Finanzasspa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccesseng
dc.rights.localAcceso abiertospa
dc.subject.keywordAutoregressive modeleng
dc.subject.keywordBayesian analysiseng
dc.subject.keywordForecasteng
dc.subject.keywordRobust prioreng
dc.titleWhat is the effect of sample and prior distributions on a Bayesian autoregressive linear model? An application to piped water consumptioneng
dc.typeinfo:eu-repo/semantics/workingPaper
dc.type.coarhttp://purl.org/coar/resource_type/c_8042
dc.type.localDocumento de trabajo de investigaciónspa
dc.type.redcolhttp://purl.org/redcol/resource_type/WP
dc.type.versioninfo:eu-repo/semantics/draft
dspace.entity.typePublication

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