NDLI: Priors for Bayesian adaptive spline smoothing

Content Provider	Springer Nature Link
Author	Yue, Yu Ryan Speckman, Paul L. Sun, Dongchu
Copyright Year	2011
Abstract	Adaptive smoothing has been proposed for curve-fitting problems where the underlying function is spatially inhomogeneous. Two Bayesian adaptive smoothing models, Bayesian adaptive smoothing splines on a lattice and Bayesian adaptive P-splines, are studied in this paper. Estimation is fully Bayesian and carried out by efficient Gibbs sampling. Choice of prior is critical in any Bayesian non-parametric regression method. We use objective priors on the first level parameters where feasible, specifically independent Jeffreys priors (right Haar priors) on the implied base linear model and error variance, and we derive sufficient conditions on higher level components to ensure that the posterior is proper. Through simulation, we demonstrate that the common practice of approximating improper priors by proper but diffuse priors may lead to invalid inference, and we show how appropriate choices of proper but only weakly informative priors yields satisfactory inference.
Starting Page	577
Ending Page	613
Page Count	37
File Format	PDF
ISSN	00203157
Journal	Annals of the Institute of Statistical Mathematics
Volume Number	64
Issue Number	3
e-ISSN	15729052
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-01-18
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Adaptive smoothing Intrinsic autoregressive Objective priors Penalized regression Posterior propriety Statistics Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability

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