Univariate Polynomial Inference by Monte Carlo Message Length Approximation

We apply the Message from Monte Carlo (MMC) algorithm to inference of univariate polynomials. MMC is an algorithm for point estimation from a Bayesian posterior sample. It partitions the posterior sample into sets of regions that contain similar models. Each region has an associated message length (given by Dowe’s MMLD approximation) and a point estimate that is representative of models in the region. The regions and point estimates are chosen so that the KullbackLeibler distance between models in the region and the associated point estimate is small (using Wallace’s FSMML Boundary Rule). We compare the MMC algorithm’s point estimation performance with Minimum Message Length [12] and Structural Risk Minimisation on a set of ten polynomial and nonpolynomial functions with Gaussian noise. The orthonormal polynomial parameters are sampled using reversible jump Markov chain Monte Carlo methods.