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General Departmental Seminar Series


Finding the knots in free-knot splines

Mary Lindstrom
Department of Biostatistics and Medical Informatics
University of Wisconsin-Madison

Fri, April 21, 2000, 12:00-1:00 pm

3285 Medical Science Center
1300 University Avenue

ABSTRACT

Regression splines (piecewise polynomials) are often used in statistical models for smooth response functions and densities. When the number and location of the joint points (or knots) are optimized, the fit is improved and the spline is a nonparametric model with locally determined smoothness. However, finding the optimal knot locations is a very difficult optimization problem. I will discuss two methods of regularizing the problem by incorporating a penalty on the knot vectors. The first is a penalized sum of squares approach and the second is a Bayesian model with a prior on the knot vectors. For this second method, I will describe a reversible jump MCMC sampler for obtaining a sample from the posterior distribution of the number and location of the knots and the spline coefficients.


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