  We develop a simulation-based method for the online updating of Gaussian
process regression and classification models. Our method exploits sequential
Monte Carlo to produce a fast sequential design algorithm for these models
relative to the established MCMC alternative. The latter is less ideal for
sequential design since it must be restarted and iterated to convergence with
the inclusion of each new design point. We illustrate some attractive ensemble
aspects of our SMC approach, and show how active learning heuristics may be
implemented via particles to optimize a noisy function or to explore
classification boundaries online.
