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Bayesian Regression with Multivariate Linear Splines
C. C. Holmes and B. K. Mallick
Journal of the Royal Statistical Society. Series B (Statistical Methodology)
Vol. 63, No. 1 (2001), pp. 3-17
Stable URL: http://www.jstor.org/stable/2680630
Page Count: 15
You can always find the topics here!Topics: Linear regression, Modeling, Linear models, Parametric models, Datasets, Statism, Simulations, Ozone, Bayesian networks, Interpretability
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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.
Journal of the Royal Statistical Society. Series B (Statistical Methodology) © 2001 Royal Statistical Society