Choice of B-splines with free parameters in the flexible discriminant analysis context
Computational Statistics & Data Analysis
Capturing Flexible Heterogeneous Utility Curves: A Bayesian Spline Approach
Management Science
Bayesian estimation and variable selection for single index models
Computational Statistics & Data Analysis
Bayesian analysis of generalized partially linear single-index models
Computational Statistics & Data Analysis
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A fully Bayesian approach to estimating cubic free-knot splines is described. A new transition kernel for a reversible jump Markov chain Monte Carlo sampler is developed including a general method for constructing proposals for conditionally linear parameters. A general prior for the knots is proposed which allows a varying amount of prior probability on knot vectors with nearly identical knots. A data-based prior is used for the conditionally linear coefficients which avoids the tendency to assign all posterior probability on the smallest model when the range of the coefficients is large compared to the variability in the data. Dimension changing moves include moves to increase/decrease the knot vector by an arbitrary number of knots which improves mixing; particularly, when the posterior for the number of knots is multi-modal. We apply the method to two data sets.