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Unpublished Paper
Spatially Adaptive Bayesian P-Splines with Heteroscedastic Errors
Johns Hopkins University, Dept. of Biostatistics Working Papers
  • Ciprian M. Crainiceanu, Johns Hokins Bloomberg School of Public Health, Department of Biostatistics
  • David Ruppert, School of Operational Research & Industrial Engineering, Cornell University
  • Raymond J. Carroll, Department of Statistics, Texas A&M University
Date of this Version

An increasingly popular tool for nonparametric smoothing are penalized splines (P-splines) which use low-rank spline bases to make computations tractable while maintaining accuracy as good as smoothing splines. This paper extends penalized spline methodology by both modeling the variance function nonparametrically and using a spatially adaptive smoothing parameter. These extensions have been studied before, but never together and never in the multivariate case. This combination is needed for satisfactory inference and can be implemented effectively by Bayesian \mbox{MCMC}. The variance process controlling the spatially-adaptive shrinkage of the mean and the variance of the heteroscedastic error process are modeled as log-penalized splines. We discuss the choice of priors and extensions of the methodology,in particular, to multivariate smoothing using low-rank thin plate splines. A fully Bayesian approach provides the joint posterior distribution of all parameters, in particular, of the error standard deviation and penalty functions. In the multivariate case we produce maps of the standard deviation and penalty functions. Our methodology can be implemented using the Bayesian software WinBUGS.

Citation Information
Ciprian M. Crainiceanu, David Ruppert and Raymond J. Carroll. "Spatially Adaptive Bayesian P-Splines with Heteroscedastic Errors" (2004)
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