JRG/1: Regression Models Beyond the Mean – A Bayesian Approach to Machine Learning

Recent progress in computer science has led to data structures of increasing size, detail and complexity in many scientific studies. In particular nowadays, where such big data applications do not only allow but also require more flexibility to overcome modelling restrictions that may result in model misspecification and biased inference, further insight in more accurate models and appropriate inferential methods is of enormous importance. This research group will therefore develop statistical tools for both univariate and multivariate regression models that are interpretable and that can be estimated extremely fast and accurate. Specifically, we aim to develop probabilistic approaches to recent innovations in machine learning in order to estimate models for huge data sets. To obtain more accurate regression models for the entire distribution we construct new distributional models that can be used for both univariate and multivariate responses. In all models we will address the issues of shrinkage and automatic variable selection to cope with a huge number of predictors, and the possibility to capture any type of covariate effect. This proposal also includes software development as well as applications in natural and social sciences (such as income distributions, marketing, weather forecasting, chronic diseases and others), highlighting its potential to successfully contribute to important facets in modern statistics and data science.