Bayesian Surface Smoothing Under Anisotropy for Count Data

• Activity Number: 424
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Subhashish Chakravarty*+
• Companies: University of Southern California
• Keywords: Bayesian ; smoothing ; anisotropy ; count data

Abstract

We propose a non-parametric approach to Bayesian surface smoothing for count data in the presence of geometric anisotropy. We use eigenfunctions generated by thin-plate splines as the basis functions of the smooth surface. Using eigenfunctions does away with having to place knots arbitrarily and the non-parametric approach provides for modeling flexibility. The smoothing parameter, the anisotropy matrix, and other parameters are simultaneously updated by a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler. Model selection is done concurrently with the parameter updates. Since the posterior distribution of the coefficients of the basis functions for any given model is available in closed form, we are able to simplify the sampling algorithm in the model selection step. We find higher values of the smoothness parameter correspond to more number of basis functions being selected. A Bayesian approach also allows us to include the results obtained from previous analysis of the same data, if any, as prior information. It also allows us to evaluate point-wise estimates of variability of the fitted surface.