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December 2016 Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression
Nadja Klein, Thomas Kneib
Bayesian Anal. 11(4): 1071-1106 (December 2016). DOI: 10.1214/15-BA983


The selection of appropriate hyperpriors for variance parameters is an important and sensible topic in all kinds of Bayesian regression models involving the specification of (conditionally) Gaussian prior structures where the variance parameters determine a data-driven, adaptive amount of prior variability or precision. We consider the special case of structured additive distributional regression where Gaussian priors are used to enforce specific properties such as smoothness or shrinkage on various effect types combined in predictors for multiple parameters related to the distribution of the response. Relying on a recently proposed class of penalised complexity priors motivated from a general set of construction principles, we derive a hyperprior structure where prior elicitation is facilitated by assumptions on the scaling of the different effect types. The posterior distribution is assessed with an adaptive Markov chain Monte Carlo scheme and conditions for its propriety are studied theoretically. We investigate the new type of scale-dependent priors in simulations and two challenging applications, in particular in comparison to the standard inverse gamma priors but also alternatives such as half-normal, half-Cauchy and proper uniform priors for standard deviations.


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Nadja Klein. Thomas Kneib. "Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression." Bayesian Anal. 11 (4) 1071 - 1106, December 2016.


Published: December 2016
First available in Project Euclid: 24 November 2015

zbMATH: 1357.62115
MathSciNet: MR3545474
Digital Object Identifier: 10.1214/15-BA983

Keywords: Kullback–Leibler divergence , Markov chain Monte Carlo simulations , penalised complexity prior , penalised splines , propriety of the posterior

Rights: Copyright © 2016 International Society for Bayesian Analysis

Vol.11 • No. 4 • December 2016
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