Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/31017
Authors: 
Fahrmeir, Ludwig
Kneib, Thomas
Year of Publication: 
2006
Series/Report no.: 
Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 510
Abstract: 
Structured additive regression comprises many semiparametric regression models such as generalized additive (mixed) models, geoadditive models, and hazard regression models within a unified framework. In a Bayesian formulation, nonparametric functions, spatial effects and further model components are specified in terms of multivariate Gaussian priors for high-dimensional vectors of regression coefficients. For several model terms, such as penalised splines or Markov random fields, these Gaussian prior distributions involve rank-deficient precision matrices, yielding partially improper priors. Moreover, hyperpriors for the variances (corresponding to inverse smoothing parameters) may also be specified as improper, e.g. corresponding to Jeffery's prior or a flat prior for the standard deviation. Hence, propriety of the joint posterior is a crucial issue for full Bayesian inference in particular if based on Markov chain Monte Carlo simulations. We establish theoretical results providing sufficient (and sometimes necessary) conditions for propriety and provide empirical evidence through several accompanying simulation studies.
Subjects: 
Bayesian semiparametric regression
Markov random fields : MSMC
penalised splines
propriety of posteriors
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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