Variational approximations in geoadditive latent Gaussian regression: mean and quantile regression
Geoadditive regression models define a comprehensive class of statistical models that allow to capture a variety of different effects on a response variable of interest, including nonlinear effects of continuous covariates and spatial effects as special cases. We develop variational approximations for Bayesian inference in geoadditive regression models to provide a computationally attractive, fast alternative to Markov chain Monte Carlo simulations. Therefore we consider the class of latent Gaussian regression models where the distribution of the response can be represented as a location-scale mixture of Gaussians such that the calculation of quasi-full conditionals in the variational approximations is considerably facilitated. As special cases, we consider mean and quantile regression and evaluate the novel variational Bayes approaches in a simulation study. As an application, we focus on the analysis of technical efficiencies of British and Welsh farms where the response variable of interest is the output produced by a farm given specific input covariates.
quantile regression markov chain monte carlo simulations variational bayes markov random fields penalized splines location-scale mixture of normals