Penalized splines, Mixed Models and Bayesian Ideas

Abstract

The paper describes the link between penalized spline smoothing and Linear Mixed Models and how these two models form a practical and theoretically interesting partnership. As offspring of this partnership one can not only estimate the smoothing parameter in a Maximum Likelihood framework but also utilize the Mixed Model technology to derive numerically handy solutions to more general questions and problems. Two particular examples are discussed in this paper. The first contribution demonstrates penalized splines and Linear Mixed Models in a classification context. Secondly, an even broader framework is pursued, mirroring the Bayesian paradigm combined with simple approximate numerical solutions for model selection. © 2010 Springer-Verlag Berlin Heidelberg.