Rao-Blackwellized sampling for batch and recursive Bayesian inference of Piecewise Affine models

Abstract

This paper addresses batch (offline) and recursive (online) Bayesian inference of Piecewise Affine (PWA) regression models. By exploiting the particular structure of PWA models, efficient Rao-Blackwellized Monte Carlo sampling algorithms are developed to approximate the joint posterior distribution of the model parameters. Only the marginal posterior of the parameters used to describe the regressor-space partition is approximated, either in a batch mode using a Metropolis–Hastings Markov-Chain Monte Carlo (MCMC) sampler, or sequentially using particle filters, while the conditional distribution of the other model parameters is computed analytically. Probability distributions for the predicted outputs given new test inputs are derived and modifications of the proposed approaches to address maximum-a-posteriori estimate are discussed. The performance of the proposed algorithms is shown via a numerical example and through a benchmark case study on data-driven modelling of the electronic component placement process in a pick-and-place machine.