Abstract

this paper is to provide a Bayesian algorithm which mimics the MARS procedure. This is done by considering the number of basis functions, along with their type (see Section 2.1), their coefficients and their form (the positions of the split points and the sign indicators) random. We treat these as additional parameters in the problem and make inference about them using the data. The problem of routine calculation of the posterior distribution of the models is addressed by designing a suitable Markov chain Monte Carlo (MCMC) reversible jump simulation algorithm as set out by Green (1995). The simulated sample contains many different MARS models with corresponding posterior weights but if a estimate for f with high predictive power is all that is required then pointwise averaging over all the models in the sample is suggested. This work is an extension to the Bayesian approach to curve fitting in one dimension given by Denison et al. (1998b) and is related to the Bayesian CART algorithms proposed by Denison et al. (1998a) and Chipman et al.

Citations