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Bayesian regression on non-parametric mixed-effect models with shape-restricted Bernstein polynomials
Authors:Jianhua Ding  Zhongzhan Zhang
Institution:1. Department of Statistics, Shanxi Datong University, Datong, People's Republic of China;2. College of Applied Sciences, Beijing University of Technology, Beijing, People's Republic of China
Abstract:We develop a Bayesian estimation method to non-parametric mixed-effect models under shape-constrains. The approach uses a hierarchical Bayesian framework and characterizations of shape-constrained Bernstein polynomials (BPs). We employ Markov chain Monte Carlo methods for model fitting, using a truncated normal distribution as the prior for the coefficients of BPs to ensure the desired shape constraints. The small sample properties of the Bayesian shape-constrained estimators across a range of functions are provided via simulation studies. Two real data analysis are given to illustrate the application of the proposed method.
Keywords:Bernstein polynomials  shape constrains  truncated normal distribution  Markov chainMonte Carlo sampler
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