Robust specification of the roughness penalty prior distribution in spatially adaptive Bayesian P-splines models
(2005) , 18 pages
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- Abstract
- We start the paper by pointing the potential important role of the prior distribution of the roughness penalty parameter in the resulting smoothness of Bayesian P-splines models (Ruppert et al. 2003 ; Lang and Brezger 2004). The recommended specification for that distribution yields models that can lack flexibility in specific circumstances. In such instances, these are shown to correspond to a frequentist P-splines model (Eilers & Marx, 1996) with a predefined and severe roughness penalty parameter, an obviously undesirable feature. We show that the specification of a hyperprior distribution for one parameter of that prior distribution provides the desired flexibility. Alternatively, a mixture prior can also be used. An extension of these two models by enabling adaptive penalties is provided. All the proposed models can be fitted quickly using the convenient Gibbs algorithm.
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Citations
Jullion, A., & Lambert, P. (2005). Robust specification of the roughness penalty prior distribution in spatially adaptive Bayesian P-splines models (Stat Discussion Paper 0534). https://hdl.handle.net/2078.5/34034