A6: Bayesian Generalized Additive Models for Location Scale and Shape

PhD student: Nadja Klein
Thesis Committee: Prof. Thomas Kneib, Prof. Tatyana Krivobokova
Graduation Date: 12/2014

Generalized additive models for location scale and shape (GAMLSS) define a flexible, semi-parametric class of regression models. While ordinary regression analyses only the effects of covariates on the mean of a response variable, GAMLSS describes more complex parameters of the underlying distribution using semi-parametric additive predictors. In contrast to quantile or expectile regression, which avoid assumptions about the underlying distribution, GAMLSS has the advantage that the effects of covariates directly impact the parameters of the underlying distribution, and are therefore easier to interpret. In particular, the scale of the responses can be directly linked to a regression specification, therefore allowing to analyse covariate-dependent scaling. However, more complex and numerically demanding likelihood-functions are a consequence. An alternative to likelihood-based estimations are efficient Markov chain Monte Carlo techniques (MCMC). Especially constructing adequate proposal densities, which automatically deliver approximations of the full conditionals, play a crucial role. The Bayesian approach will be compared to existing likelihood-based estimations, where the former one has the advantage that the smoothing parameters are part of the procedure, and do not have to be estimated separately.

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