Shape restricted regression with random Bernstein polynomials
By I. Chang, Li-Chu Chien, Chao A. Hsiung, Chi-Chung Wen, Yuh-Jenn Wu. 2007
55 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e1c54b93d0e8b4087615770ff5cbe84a5489f65b
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In Artificial Intelligence
- Sujit Kumar Ghosh
- S. M. Curtisa
- S. Ghoshb
- Lauren Hannah
- David B. Dunson
- David M. Blei
- Lawrence Carin
- Qiang Yang
In Computer Vision and Pattern Recognition
In Geometry and Topology
Citations in the corpus
- Multivariate convex regression with adaptive partitioning (2011, methodology): “In other methods, Birke & Dette (2007) used convexity constrained kernel regression; Chang et al. (2007) used a random Bernstein polynomial prior with constrained parameters; and Koushanfar et al.”
- Bayesian Spatial Quantile Regression (2013, unknown): “However, as M increases, the Bernstein polynomials basis with these constraints induces a prior with dense support on the space of continuous monotone functions from [0; 1] R (Chang et al., 2007).”
- A variable selection approach to monotonic regression with Bernstein polynomials (2011, methodology): “A first attempt [10] would be to define a continuous prior (e.”
- Using Instrumental Variables for Inference About Policy Relevant Treatment Effects (2018, unknown): “Derivations of these properties can be found in Chang et al. (2007) and McKay Curtis and Ghosh (2011).”