Automatic Bayesian knot placement for spline fitting

We propose a Bayesian model for automatically determining knot placement in spline modelling. The random variables of the model are the number of knots and their locations, which we seek to estimate via a simulated annealing form of the reversible jump Markov chain Monte Carlo sampler. This novel technique has the ability to maximise the joint posterior distribution of the number of knots and their locations, without becoming stranded on local maxima. We provide results which verify the effectiveness of the proposed technique, in accurately fitting a non-uniform, cubic spline to data, whilst maintaining a relatively small number of knots