Bayesian Local Extrema Splines

• Activity Number: 534
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Matthew Wheeler* and David Dunson and Amy Herring
• Companies: NIOSH/CDC and Duke University and The University of North Carolina at Chapel Hill
• Keywords: Constrained Function Estimation ; Nonparametric Function Estimation ; Shape Constraint ; M-Splines

Abstract

We consider the problem of shape restricted nonparametric regression on a closed set, where it is reasonable to assume the function has no more than H local extrema interior to this set. Following a Bayesian approach, we develop a nonparametric prior over a novel class of local extrema splines. This approach is shown to be consistent when modeling any continuously differentiable function within the class of functions considered, and is used to develop methods for hypothesis testing on the shape of the curve, where the shape of the curve is defined by the number and type of the extrema. Sampling algorithms are developed and the method is applied in simulation studies as well as a data example where the shape of the curve is of interest.