Automatic Bayesian Curve Fitting
Journal of the Royal Statistical Society Series B (Statistical Methodology)Published 1 July 1998Open access
D. G. T. Denison, Bani K. Mallick, A. F. M. Smith
Citations403
SJR quartileQ1
SJR score3.31
SNIP2.48
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TL;DR
A method of estimating a variety of curves by a sequence of piecewise polynomials, motivated by a Bayesian model and an appropriate summary of the resulting posterior distribution, is proposed, successful in giving good estimates for ‘smooth’ functions.
Abstract
Summary A method of estimating a variety of curves by a sequence of piecewise polynomials is proposed, motivated by a Bayesian model and an appropriate summary of the resulting posterior distribution. A joint distribution is set up over both the number and the position of the knots defining the piecewise polynomials. Throughout we use reversible jump Markov chain Monte Carlo methods to compute the posteriors. The methodology has been successful in giving good estimates for ‘smooth’ functions (i.e. continuous and differentiable) as well as functions which are not differentiable, and perhaps not even continuous, at a finite number of points. The methodology is extended to deal with generalized additive models.
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