Automatic Bayesian curve fitting. (English) Zbl 0907.62031

Denison, D. G. T.; Mallick, B. K.; Smith, A. F. M.

J. R. Stat. Soc., Ser. B, Stat. Methodol. 60, No. 2, 333-350 (1998).

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.

MSC:

62F15	Bayesian inference
62J02	General nonlinear regression
65C99	Probabilistic methods, stochastic differential equations

Keywords:

additive models; back-fitting algorithm; least squares regression; splines; unsmooth functions; piecewise polynomials; reversible jump Markov chain Monte Carlo methods