What is the effect of sample and prior distributions on a Bayesian autoregressive linear model? An application to piped water consumption
| dc.contributor.author | Ramírez Hassan, Andrés | |
| dc.contributor.author | Cardona Jiménez, Jhonatan | |
| dc.contributor.author | Pericchi Guerra, Raul | |
| dc.contributor.eafitauthor | aramir21@eafit.edu.co | |
| dc.contributor.eafitauthor | jcardonj@dme.ufrj.br | |
| dc.contributor.eafitauthor | lrpericchi@uprrp.edu | |
| dc.coverage.spatial | Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees | eng |
| dc.date.accessioned | 2014-08-01T20:58:17Z | |
| dc.date.available | 2014-08-01T20:58:17Z | |
| dc.date.issued | 2014-07-23 | |
| dc.description.abstract | In 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.identifier.jel | C11 | |
| dc.identifier.jel | C53 | |
| dc.identifier.uri | http://hdl.handle.net/10784/2857 | |
| dc.language.iso | eng | eng |
| dc.publisher | Universidad EAFIT | spa |
| dc.publisher.department | Escuela de Economía y Finanzas | spa |
| dc.rights.accessrights | info:eu-repo/semantics/openAccess | eng |
| dc.rights.local | Acceso abierto | spa |
| dc.subject.keyword | Autoregressive model | eng |
| dc.subject.keyword | Bayesian analysis | eng |
| dc.subject.keyword | Forecast | eng |
| dc.subject.keyword | Robust prior | eng |
| dc.title | What is the effect of sample and prior distributions on a Bayesian autoregressive linear model? An application to piped water consumption | eng |
| dc.type | workingPaper | eng |
| dc.type | info:eu-repo/semantics/workingPaper | eng |
| dc.type.hasVersion | draft | eng |
| dc.type.local | Documento de trabajo de investigación | spa |
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