Bayesian additive models for location, scale, and shape (and beyond) provide a general framework for distributional regression. Accompanied by the R package bamlss.
Nikolaus Umlauf, Nadja Klein, Achim Zeileis (2018).
“BAMLSS: Bayesian Additive Models for Location, Scale and Shape (and Beyond).”
Journal of Computational and Graphical Statistics. Forthcoming.
[ pdf ]
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 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, as well as a Cox model for continuous
time with space-time interactions.
Censored heteroscedastic precepitation climatology, with spatially-varying seasonal effects,
spatial main effects, and predicted average precipitation for target date.