Locally adaptive Bayesian P-splines with a Normal-Exponential-Gamma prior

Locally adaptive Bayesian P-splines with a Normal-Exponential-Gamma prior

The necessity to replace smoothing approaches with a global amount of smoothing arises in a variety of situations such as effects with highly varying curvature or effects with discontinuities. We present an implementation of locally adaptive spline smoothing using a class of heavy-tailed shrinkage priors. These priors utilize scale mixtures of normals with locally varying exponential-gamma dist...

Spatially Adaptive Bayesian Penalized Regression Splines (P-splines)

In this paper we study penalized regression splines (P-splines), which are low–order basis splines with a penalty to avoid undersmoothing. Such P–splines are typically not spatially adaptive, and hence can have trouble when functions are varying rapidly. Our approach is to model the penalty parameter inherent in the P–spline method as a heteroscedastic regression function. We develop a full Bay...

Robust specification of the roughness penalty prior distribution in spatially adaptive Bayesian P-splines models

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...

Bayesian P-Splines

Spatially Adaptive Bayesian Regression Splines

In this paper we study penalized regression splines (P-splines), which are low–order basis function splines with a penalty to avoid undersmoothing. Such P–splines are typically not spatially adaptive, and hence can have trouble when functions are varying rapidly. While frequentist methods are available to address this issue, no Bayesian techniques have been developed. Our approach is to model t...