VIBASS2 - Invited Course

This course (12 hours) is provided by Nadja Klein, Research Feodor-Lynen-Fellow (Humboldt Foundation), University of Melbourne (Australia) and Nikolaus Umlauf Assistant Professor in Statistics, Universität Innsbruck (Austria). Both are coauthors of the R package BayesX

• Course on Bayesian modeling with BayesX

• Instructors

  

  Nadja Klein, Feodor-Lynen-Fellow (Humboldt Foundation), University of Melbourne (Australia). Nadja pursued research in the areas of Bayesian statistics, computational methods, machine learning with a focus on developing distributional statistical and econometric methods for large and complex datasets. These can be used for modelling highly nonlinear data and to solve important and recurrent problems that arise economy, ecology and further applied areas. Nadja is co-author of the R package bamlss and the C++ library BayesX.

  Nikolaus Umlauf Assistant Professor in Statistics, Universität Innsbruck (Austria). His research focuses on complex (Bayesian) distributional regression models that can combine commonly used approaches for modeling highly nonlinear data with methods used in machine learning. The applications of this modeling framework are diverse, from economic problems to meteorological, medical and remote sensing, etc. He is co-author of the R package bamlss, the C++ library BayesX and its corresponding R interface package R2BayesX, as well as the the R package exams.

• Audience

  Statisticians and applied researchers with strong interest in quantitative analysis

• Abstract

  This course is aimed to statisticians and applied researchers who are interested in learning about various types of Additive Regression using the R packages BayesX (http://www.BayesX.org) and bamlss (https://cran.r-project.org/package=bamlss). Additive regression, i.e., penalised spline smoothing and structured additive distributional regression models provide a simple yet flexible possibility to introduce nonlinear covariate effects in any type of regression models. In a Bayesian formulation, the penalty terms transform into specific prior distributions that enforce appropriate smoothness of the estimates. The short course will focus on fundamental construction principles of structured additive regression models under Bayesian perspective.

  Usual exponential family regression models solely focus on modelling the conditional mean of a response distribution dependent on a set of covariates. While this entails easy interpretation, the basic assumption that higher order moments of the conditional distribution are constant for all observations might be too restrictive in complex data structures and thus lead to false conclusions drawn from the models. Distributional regression combines the flexibility in terms of structured additive predictors developed for mean regression models with an increased flexibility in terms of the parametric response distribution that can be assumed. Examples for the latter are zero-inflated count data models, location-scale models or models for multivariate, correlated responses. After reviewing concepts of penalised spline smoothing and geoadditive regression, this course treats distributional regression for different types of univariate responses as well as multivariate responses. Variable selection and model choice strategies will be addressed.

  The course will cover models in different fields of statistics along real data examples to illustrate the potentials of these models. The statistical software used in the course will be R. The main packages will be BayesX and bamlss. Copies of the training materials will be provided as well as data examples with code. Important Bayesian tools like hyperprior choices or convergence diagnosis for Bayesian inference will be introduced as well. Lecture sessions will be followed by hands-on practical sessions, where attendants will be able to fit different models in practice using the two R-packages.

• Table of Contents

  • Introduction to Geoadditive Regression

  • Basics on smoothing regression

  • Frequentist and Bayesian perspectives.

  • Illustrations through real data examples.

  • Basic Concepts of Distributional Regression

  • Univariate Distributional Regression

  • Model Choice and Variable Selection

  • Multivariate Distributional Regression

  • Illustrative Examples

• References

  • Umlauf, N., Klein, N. and Zeileis, A. (2017) BAMLSS: Bayesian Additive Models forLocation, Scale and Shape (and Beyond). To appear in Journal of Computational and Graphical Statistics.

  • Kammann, E. E. and Wand, M. P. (2003). Geoadditive models, Journal of the Royal Statistical Society: Series C (Applied Statistics) 52: 1–18.

  • Fahrmeir, Kneib & Lang (2013): Regression: Models, Methods and Applications, Springer.

  • Fahrmeir, L., Kneib, T.: Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data. Oxford University Press, New York (2011)

  • Eilers, P. H. and Marx, B. D. (1996). Flexible smoothing using B-splines and penalized Likelihood, Statistical Science 11: 89–121.

  • Wood, S.N.: Generalized Additive Models : An Introduction with R. Chapman & Hall/CRC, New York/Boca Raton (2006)

  • Klein, N. and Kneib, T. (2016) Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Bayesian Analysis, 11, 1071-1106, doi:10.1214/15-BA983.

  • Klein, N., Kneib, T. and Lang, S. (2015) Bayesian Generalized Additive Models for Location, Scale and Shape for Zero-Inflated and Overdispersed Count Data. Journal of the American Statistical Association, 110, 405-419

  • Klein, N., Kneib, T., Klasen, S. and Lang, S. (2015) Bayesian Structured Additive Distributional Regression for Multivariate Responses. Journal of the Royal Statistical Society: Series C, 64, 569-591

  • Klein, N., Kneib, T., Lang, S. and Sohn, A. (2015) Bayesian Structured Additive Distributional Regression with an Application to Regional Income Inequality in Germany. Annals of Applied Statistics, 9, 1024-1052.