Bayesian local extremum splines

• 成果类型: Article
• 署名作者: Wheeler, M. W.; Dunson, D. B.; Herring, A. H.
• 署名单位: Centers for Disease Control & Prevention - USA; National Institute for Occupational Safety & Health (NIOSH); Duke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asx039
• 发表日期: 2017
• 页码: 939952
• 关键词: regression splines; isotonic regression; linear-models; shape; MONOTONICITY; inference; curve

摘要

We consider shape- restricted nonparametric regression on a closed set X. R, where it is reasonable to assume that the function has no more than H local extrema interior to X. Following a Bayesian approach we develop a nonparametric prior over a novel class of local extremum splines. This approach is shown to be consistent when modelling any continuously differentiable function within the class considered, and we use it to develop methods for testing hypotheses on the shape of the curve. Sampling algorithms are developed, and the method is applied in simulation studies and data examples where the shape of the curve is of interest.