Bayesian Structured Additive Distributional Regression
AbstractIn this paper, we propose a generic Bayesian framework for inference in distributional regression models in which each parameter of a potentially complex response distribution and not only the mean is related to a structured additive predictor. The latter is composed additively of a variety of different functional effect types such as nonlinear effects, spatial effects, random coefficients, interaction surfaces or other (possibly non-standard) basis function representations. To enforce specific properties of the functional effects such as smoothness, informative multivariate Gaussian priors are assigned to the basis function coefficients. Inference is then based on efficient Markov chain Monte Carlo simulation techniques where a generic procedure makes use of distribution-specific iteratively weighted least squares approximations to the full conditionals. We study properties of the resulting model class and provide detailed guidance on practical aspects of model choice including selecting an apropriate response distribution and predictor specification. The importance and flexibility of Bayesian structured additive distributional regression to estimate all parameters as functions of explanatory variables and therefore to obtain more realistic models, is exemplified in two applications with complex response distributions.
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Bibliographic InfoPaper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2013-23.
Length: 65 pages
Date of creation: Oct 2013
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Web page: http://www.uibk.ac.at/fakultaeten/volkswirtschaft_und_statistik/index.html.en
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generalised additive models for location scale and shape; iteratively weighted least squares proposal; Markov chain Monte Carlo simulation; penalised splines; semiparametric regression;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-10-11 (All new papers)
- NEP-ECM-2013-10-11 (Econometrics)
- NEP-ORE-2013-10-11 (Operations Research)
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- Alexander Razen & Wolfgang Brunauer & Nadja Klein & Thomas Kneib & Stefan Lang & Nikolaus Umlauf, 2014. "Statistical Risk Analysis for Real Estate Collateral Valuation using Bayesian Distributional and Quantile Regression," Working Papers 2014-12, Faculty of Economics and Statistics, University of Innsbruck.
- Nadja Klein & Michel Denuit & Stefan Lang & Thomas Kneib, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," Working Papers 2013-24, Faculty of Economics and Statistics, University of Innsbruck.
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