An implementation of locally adaptive penalized spline smoothing using a class of heavy-tailed shrinkage priors for the estimation of functional forms with highly varying curvature or discontinuities is presented. These priors utilize scale mixtures of normals with locally varying exponential-gamma distributed variances for the differences of the P-spline coefficients. A fully Bayesian hierarchical structure is derived with inference about the posterior being based on Markov Chain Monte Carlo techniques. Three increasingly flexible and automatic approaches are introduced to estimate the spatially varying structure of the variances. An extensive simulation study for Gaussian, Poisson, and Binomial responses shows that the performance of this approach on a number of benchmark functions is competitive to that of previous approaches. Results from applications with Gaussian and Poisson responses support the simulation results. © 2009 Elsevier B.V. All rights reserved.
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