Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression

By N. Klein, Thomas Kneib. 2016

71 citations recorded by the source corpus.

. 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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/abd004559efbbb08884a4d14e0db40d6a6767b77

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Citations in the corpus

Constructing Priors that Penalize the Complexity of Gaussian Random Fields (2015, methodology): “This setting is similar to structured additive regression models where Klein and Kneib (2016) have shown that the penalized complexity (PC) prior framework developed by Simpson et al. (2017) behaves well when used for the components of the models.”
Bayesian Computing with INLA: A Review (2016, methodology): “…age-period-cohort models (Riebler and Held, 2016), Bayesian P-splines (Ventrucci and Rue, 2016), structured additive distributional regression (Klein and Kneib, 2016), Gaussian ﬁelds in spatial statistics (Fuglstad et al., 2016), modeling monthly maxima of instantaneous ﬂow (Ferkingstad et…”
The Prior Can Often Only Be Understood in the Context of the Likelihood (2017, methodology): “They did this using a localized version of the Kullback-Leibler divergence, which seems to work reasonably well in the cases that have been examined (Klein and Kneib, 2016).”