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December 2011 A Computational Bayesian Method for Estimating the Number of Knots In Regression Splines
Minjung Kyung
Bayesian Anal. 6(4): 793-828 (December 2011). DOI: 10.1214/11-BA629

Abstract

To determine the size of the drug-involved offender population that could be served effectively and efficiently by partnerships between courts and treatment in the United States, a synthetic dataset is created by Bhati and Roman (2009). Because of hidden structure and aggregation necessary to create variables, there exists latent variance that can not be explained fully by a normal random effect model. Semiparametric regression is a well-known and frequently used tool to capture the functional dependence between variables with fixed effect parametric and nonlinear regression. A new Gibbs sampler is developed here for the number and positions of knots in regression splines by expressing semiparametric regression as a linear mixed model with a random effect term for the basis functions. Our Gibbs sampler exploits the properties of the multinomial-Dirichlet distribution, and is shown to be an improvement, in terms of operator norm and efficiency, over add/delete one MCMC algorithms. We find that the Dirichlet distribution with small values of the parameters results in a smaller number of knots and, in general, good fit to the data. This approach is shown to reveal previously unseen structures in the synthetic dataset of Bhati and Roman.

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Minjung Kyung. "A Computational Bayesian Method for Estimating the Number of Knots In Regression Splines." Bayesian Anal. 6 (4) 793 - 828, December 2011. https://doi.org/10.1214/11-BA629

Information

Published: December 2011
First available in Project Euclid: 13 June 2012

zbMATH: 1330.62194
MathSciNet: MR2869965
Digital Object Identifier: 10.1214/11-BA629

Keywords: Bayesian Semiparametric Regression , Multinomial-Dirichlet distribution , regression splines

Rights: Copyright © 2011 International Society for Bayesian Analysis

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Vol.6 • No. 4 • December 2011
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