A primer on Bayesian distributional regression

Abstract: Bayesian methods have become increasingly popular in the past two decades. With the constant rise of computational power, even very complex models can be estimated on virtually any modern computer. Moreover, interest has shifted from conditional mean models to probabilistic distributional models capturing location, scale, shape and other aspects of a response distribution, where covariate effects can have flexible forms, for example, linear, non-linear, spatial or random effects. This tutorial article discusses how to select models in the Bayesian distributional regression setting, how to monitor convergence of the Markov chains and how to use simulation-based inference also for quantities derived from the original model parametrization. We exemplify the workflow using daily weather data on (a) temperatures on Germany's highest mountain and (b) extreme values of precipitation for the whole of Germany.