Spatially Adaptive Nonparametric Binary Regression

• Activity Number: 211
• Type: Invited
• Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Sally A. Wood*+ and Robert Kohn and Martin Tanner and Wenxin Jiang
• Companies: Australian Graduate School of Management and University of New South Wales and Northwestern University and Northwestern University
• Keywords: Bayesian analysis ; Markov chain Monte Carlo ; Mixture-of-Experts ; Model averaging ; Reversible jump ; Thin plate splines

Abstract

This paper presents a Bayesian method for estimating a binary regression without assuming its functional form is known. The binary regression is modeled as a mixture of binary probit regressions with the argument of each component probit regression having a thin plate spline prior. The model is made spatially adaptive by allowing the component weights to depend on the covariates and the thin plate spline priors to have differing smoothing parameters. The Bayesian approach allows for models with differing numbers of components, and the estimation of the regression function is made statistically efficient by taking a weighted average of the posterior means of the individual models. The estimation is carried out using a Markov chain Monte Carlo simulation method that requires the introduction of two new conditions to make it practical. The results of a simulation study are reported and show that the posterior mean estimator obtained by our method outperforms the single spline estimator when the function is spatially heterogeneous. It also shows our method is as good as the single spline estimator when the function is spatially homogenous.