AUTOMATIC BAYESIAN CURVE-FITTING

A method of estimating a variety of curves by a sequence of piecewise polynomials is proposed, motivated by a Bayesian model and an appropri ate summary of the resulting posterior distribution. A joint distribut ion is set up over both the number and the position of the knots defin ing the piecewise polynomials. Throughout we use reversible jump Marko v 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 o f points. The methodology is extended to deal with generalized additiv e models.