Bayesian Local Extremum Splines

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Citation

Wheeler, Matthew W.; Dunson, David B.; & Herring, Amy H. (2017). Bayesian Local Extremum Splines. Biometrika, 104(4), 939-952. PMCID: PMC5798493

Abstract

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.

URL

http://dx.doi.org/10.1093/biomet/asx039

Reference Type

Journal Article

Year Published

2017

Journal Title

Biometrika

Author(s)

Wheeler, Matthew W.
Dunson, David B.
Herring, Amy H.

PMCID

PMC5798493