Bayesian Local Extremum Splines

Wheeler, Matthew W.; Dunson, David B.; & Herring, Amy H. (Forthcoming). Bayesian Local Extremum Splines. Biometrika. PMCID: PMC5798493

Wheeler, Matthew W.; Dunson, David B.; & Herring, Amy H. (Forthcoming). Bayesian Local Extremum Splines. Biometrika. PMCID: PMC5798493

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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.




JOUR



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



Forthcoming


Biometrika











PMC5798493


10725

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