dc.contributor.author Padellini, Tullia dc.contributor.author Rue, Haavard dc.date.accessioned 2018-04-19T10:45:31Z dc.date.available 2018-04-19T10:45:31Z dc.date.issued 2018-04-10 dc.identifier.uri http://hdl.handle.net/10754/627566 dc.description.abstract Quantile regression is a class of methods voted to the modelling of conditional quantiles. In a Bayesian framework quantile regression has typically been carried out exploiting the Asymmetric Laplace Distribution as a working likelihood. Despite the fact that this leads to a proper posterior for the regression coefficients, the resulting posterior variance is however affected by an unidentifiable parameter, hence any inferential procedure beside point estimation is unreliable. We propose a model-based approach for quantile regression that considers quantiles of the generating distribution directly, and thus allows for a proper uncertainty quantification. We then create a link between quantile regression and generalised linear models by mapping the quantiles to the parameter of the response variable, and we exploit it to fit the model with R-INLA. We extend it also in the case of discrete responses, where there is no 1-to-1 relationship between quantiles and distribution's parameter, by introducing continuous generalisations of the most common discrete variables (Poisson, Binomial and Negative Binomial) to be exploited in the fitting. dc.publisher arXiv dc.relation.url http://arxiv.org/abs/1804.03714v1 dc.relation.url http://arxiv.org/pdf/1804.03714v1 dc.rights Archived with thanks to arXiv dc.title Model-based Quantile Regression for Discrete Data dc.type Preprint dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Statistics Program dc.eprint.version Pre-print dc.contributor.institution Dipartimento di Scienze Statistiche, Sapienza Universita di Roma dc.identifier.arxivid 1804.03714 kaust.person Rue, Haavard refterms.dateFOA 2018-06-14T05:55:11Z
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