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We present a Bayesian analysis of a piecewise linear model constructed using basis functions which generalizes the univariate linear spline to higher dimensions. Prior distributions are adopted on both the number and the locations of the splines, which leads to a model averaging approach to prediction with predictive distributions that take into account model uncertainty. Conditioning on the data produces a Bayes local linear model with distributions on both predictions and local linear parameters. The method is spatially adaptive and covariate selection is achieved by using splines of lower dimension than the data.

Original publication

DOI

10.1111/1467-9868.00272

Type

Journal article

Journal

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Publication Date

01/01/2001

Volume

63

Pages

3 - 17