Institute of Mathematical Statistics Lecture Notes - Monograph Series

Shape restricted regression with random Bernstein polynomials

I-Shou Chang, Li-Chu Chien, Chao A. Hsiung, Chi-Chung Wen, and Yuh-Jenn Wu

Full-text: Open access


Shape restricted regressions, including isotonic regression and concave regression as special cases, are studied using priors on Bernstein polynomials and Markov chain Monte Carlo methods. These priors have large supports, select only smooth functions, can easily incorporate geometric information into the prior, and can be generated without computational difficulty. Algorithms generating priors and posteriors are proposed, and simulation studies are conducted to illustrate the performance of this approach. Comparisons with the density-regression method of Dette et al. (2006) are included.

Chapter information

Regina Liu, William Strawderman and Cun-Hui Zhang, eds., Complex Datasets and Inverse Problems: Tomography, Networks and Beyond (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 187-202

First available in Project Euclid: 4 December 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 62F15: Bayesian inference 62G08: Nonparametric regression
Secondary: 65D10: Smoothing, curve fitting

Bayesian concave regression Bayesian isotonic regression geometric prior Markov chain Monte Carlo Metropolis-Hastings reversible jump algorithm

Copyright © 2007, Institute of Mathematical Statistics


Chang, I-Shou; Chien, Li-Chu; Hsiung, Chao A.; Wen, Chi-Chung; Wu, Yuh-Jenn. Shape restricted regression with random Bernstein polynomials. Complex Datasets and Inverse Problems, 187--202, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000157.

Export citation