A Novel Nonparametric Prior Based on Transformed Bernstein Polynomial

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yuhui Chen*+ and Timothy Hanson
• Companies: and University of South Carolina
• Keywords: Tansformed Berntein Polynomial Priors ; Density Estimation ; Accelerated Hazard Model ; Time-dependent Covariates

Abstract

We propose a transformed Bernstein polynomial that is centered at standard parametric families, such as Weibull. As such, this class provides an extremely convenient way towards creating a Bayesian non-parametric prior for smooth densities, blending the merits of parametric and non-parametric methods. This prior gives very smooth densities that are amenable to standard estimation approaches; for example optimization methods in SAS or R can yield the posterior mode and asymptotic covariance matrix. This novel nonparametric prior is emplyed in the accelerated hazard model, which is further generalized to time-dependent covariates and a joint longitudinal / accelerated hazard model.