Automatic Bayesian curve ®tting
نویسندگان
چکیده
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 de®ning 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 ®nite number of points. The methodology is extended to deal with generalized additive models.
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