Modeling Infant Mortality Data Using Bayesian Estimation with Bernstein Polynomials

• Activity Number: 73
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jiangdian Wang*+ and Sujit Kumar Ghosh
• Companies: North Carolina State University and North Carolina State University
• Keywords: Nonparametric Regression ; Shape-restricted Regresson ; Bernstein Polynomial ; Reversible Jump Markov Chain Monte Carlo ; Bayesian Method

Abstract

The estimation of shape-restricted regression curves is challenging for multivariate predictors, especially for functions with compact support. This article proposes a Bayesian framework using multivariate Bernstein polynomials and Reversible Jump Markov Chain Monte Carlo methods. Our proposed method is shown to be computationally attractive and universally consistent under some mild regularity conditions. The algorithms generating priors and posteriors are proposed, and simulation studies are conducted to illustrate the performance of this approach. Our approach is applied to a real data that investigates the underlying decreasing trend of the regression function relating the level of Expenditure Per Capita and Adult Literacy Rate to the response variable Infant Mortality Rate.