Bayesian Analysis

Adaptive Priors Based on Splines with Random Knots

Eduard Belitser and Paulo Serra

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Abstract

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.

Article information

Source
Bayesian Anal., Volume 9, Number 4 (2014), 859-882.

Dates
First available in Project Euclid: 21 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.ba/1416579182

Digital Object Identifier
doi:10.1214/14-BA879

Mathematical Reviews number (MathSciNet)
MR3293959

Zentralblatt MATH identifier
1327.62130

Keywords
Adaptive prior Bayesian non-parametric optimal contraction rate spline random knots

Citation

Belitser, Eduard; Serra, Paulo. Adaptive Priors Based on Splines with Random Knots. Bayesian Anal. 9 (2014), no. 4, 859--882. doi:10.1214/14-BA879. https://projecteuclid.org/euclid.ba/1416579182


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