Open Access
Translator Disclaimer
June 2021 Bayesian Effect Selection in Structured Additive Distributional Regression Models
Nadja Klein, Manuel Carlan, Thomas Kneib, Stefan Lang, Helga Wagner
Author Affiliations +
Bayesian Anal. 16(2): 545-573 (June 2021). DOI: 10.1214/20-BA1214


We establish Bayesian effect selection for the broad class of structured additive distributional regression models using a spike and slab prior specification with scaled beta prime marginals for the importance parameters of blocks of regression coefficients. This enables us to model and select effects in all distributional parameters, such as location, scale, skewness or correlation parameters, for arbitrary distributions. The regression specifications encompass various effect types such as non-linear or spatial effects. Our spike and slab prior relies on a parameter expansion that separates blocks of regression coefficients into overall scalar importance parameters and vectors of standardised coefficients, and yields effective shrinkage and good sampling performance. Using constrained priors, it is possible to implement effect decompositions, where, for example, a non-linear effect can be decomposed into a linear component and the non-linear deviation from this linear effect; and to select both separately. We investigate some shrinkage properties, propose a way of eliciting prior hyperparameters and provide full posterior inference through Markov Chain Monte Carlo simulations. Using both simulated and real data sets, we show that our approach is applicable for data with various functional covariate effects, multilevel predictors and non-standard response distributions, such as bivariate Gaussian or zero-inflated Poisson.


We thank a referee, the Associate Editor, the Editor-in-Chief and the Editorial Board for their careful reading of our paper and helpful comments.


Download Citation

Nadja Klein. Manuel Carlan. Thomas Kneib. Stefan Lang. Helga Wagner. "Bayesian Effect Selection in Structured Additive Distributional Regression Models." Bayesian Anal. 16 (2) 545 - 573, June 2021.


Published: June 2021
First available in Project Euclid: 16 June 2020

Digital Object Identifier: 10.1214/20-BA1214

Keywords: parameter expansion , penalised splines , prior elicitation , scaled beta prime distribution , shrinkage properties


Vol.16 • No. 2 • June 2021
Back to Top