Reference priors for shrinkage and smoothing parameters
Authors:
Angelika van der Linde
Affiliation:
Department of Mathematics and Statistics, KB, JCMB, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ Scotland, UK
Abstract:
A reference prior and corresponding reference posteriors are derived for a basic Normal variance components model with two components. Different parameterizations are considered, in particular one in terms of a shrinkage or smoothing parameter. Earlier results for the one-way ANOVA setting are generalized and a broad range of applications of the general results is indicated. Numerical examples of application to spline smoothing are given for illustration and the results compared with other well-known techniques considered to be “non-informative” about the smoothing parameter.