Bayesian estimation of free-knot splines using reversible jumps

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. (C) 2002 Elsevier Science B.V. All rights reserved.