Bayesian Functional Data Fitting with a Transformed B-Spline Basis

• Activity Number: 685
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Songqiao Huang* and David Hitchcock
• Companies: University of South Carolina and University of South Carolina
• Keywords: Bayesian ; B-splines ; Functional Data ; Smoothing ; Warping

Abstract

Data fitting is of great significance in functional data analysis, since the fitting results directly affect any potential statistical analysis that follows. Among many currently popular basis systems, the system of B-spline functions is frequently used to fit non-periodic data. In this paper, an alternative Bayesian method is proposed to use transformed basis functions obtained via a domain-warping process based on the existing B-spline functions to achieve better fit of functional data, compared with the fit via ordinary B-splines. The Gibbs sampling method augmented by the Metropolis-Hastings algorithm is employed. Based on a simulation study, the fit of simulated functional data using our approach is better than the fit based on an equivalent number of B-spline functions, especially when the data is non-homogeneous in nature.