Bayesian Gaussian processes for sequential prediction, optimisation and quadrature

We develop a family of Bayesian algorithms built around Gaussian processes for various problems posed by sensor networks. We firstly introduce an iterative Gaussian process for multi-sensor inference problems, and show how our algorithm is able to cope with data that may be noisy, missing, delayed and/or correlated. Our algorithm can also effectively manage data that features changepoints, such as sensor faults. Extensions to our algorithm allow us to tackle some of the decision problems faced in sensor networks, including observation scheduling. Along these lines, we also propose a general method of global optimisation, Gaussian process global optimisation (GPGO), and demonstrate how it may be used for sensor placement. Our algorithms operate within a complete Bayesian probabilistic framework. As such, we show how the hyperparameters of our system can be marginalised by use of Bayesian quadrature, a principled method of approximate integration. Similar techniques also allow us to produce full posterior distributions for any hyperparameters of interest, such as the location of changepoints. We frame the selection of the positions of the hyperparameter samples required by Bayesian quadrature as a decision problem, with the aim of minimising the uncertainty we possess about the values of the integrals we are approximating. Taking this approach, we have developed sampling for Bayesian quadrature (SBQ), a principled competitor to Monte Carlo methods. We conclude by testing our proposals on real weather sensor networks. We further benchmark GPGO on a wide range of canonical test problems, over which it achieves a significant improvement on its competitors. Finally, the efficacy of SBQ is demonstrated in the context of both prediction and optimisation.This thesis is not currently available in OR