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December 2014 Adaptive Priors Based on Splines with Random Knots
Eduard Belitser, Paulo Serra
Bayesian Anal. 9(4): 859-882 (December 2014). DOI: 10.1214/14-BA879


Splines are useful building blocks when constructing priors on nonparametric models indexed by functions. Recently it has been established in the literature that hierarchical adaptive priors based on splines with a random number of equally spaced knots and random coefficients in the B-spline basis corresponding to those knots lead, under some conditions, to optimal posterior contraction rates, over certain smoothness functional classes. In this paper we extend these results for when the location of the knots is also endowed with a prior. This has already been a common practice in Markov chain Monte Carlo applications, but a theoretical basis in terms of adaptive contraction rates was missing. Under some mild assumptions, we establish a result that provides sufficient conditions for adaptive contraction rates in a range of models, over certain functional classes of smoothness up to the order of the splines that are used. We also present some numerical results illustrating how such a prior adapts to inhomogeneous variability (smoothness) of the function in the context of nonparametric regression.


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Eduard Belitser. Paulo Serra. "Adaptive Priors Based on Splines with Random Knots." Bayesian Anal. 9 (4) 859 - 882, December 2014.


Published: December 2014
First available in Project Euclid: 21 November 2014

zbMATH: 1327.62130
MathSciNet: MR3293959
Digital Object Identifier: 10.1214/14-BA879

Rights: Copyright © 2014 International Society for Bayesian Analysis


Vol.9 • No. 4 • December 2014
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