BAMLSS: Bayesian additive models for location, scale and shape (and beyond)

Bayesian analysis provides a convenient setting for the estimation of complex generalized additive regression models (GAMs). Since computational power has tremendously increased in the past decade it is now possible to tackle complicated inferential problems, e.g., with Markov chain Monte Carlo simulation, on virtually any modern computer. This is one of the reasons why Bayesian methods have become increasingly popular, leading to a number of highly specialized and optimized estimation engines and with attention shifting from conditional mean models to probabilistic distributional models capturing location, scale, shape (and other aspects) of the response distribution. In order to embed many different approaches suggested in literature and software, a unified modeling architecture for distributional GAMs is established that exploits the general structure of these models and encompasses many di↵erent response distributions, estimation techniques (posterior mode or posterior mean), and model terms (fixed, random, smooth, spatial, . . . ). It is shown that within this framework implementing algorithms for complex regression problems, as well as the integration of already existing software, is relatively straightforward. The usefulness is emphasized with two complex and computationally demanding application case studies: a large daily precipitation climatology based on more than 1.2 million observations from more than 50 meteorological stations, as well as a Cox model for continuous time with space-time interactions on a data set with over five thousand “individuals”.