Gaussian Processes for Prediction

We propose a powerful prediction algorithm built upon Gaussian processes (GPs). They are particularly useful for their flexibility, facilitating accurate prediction even in the absence of strong physical models. GPs further allow us to work within a complete Bayesian probabilistic framework. As such, we show how the hyperparameters of our system can be marginalised by use of Bayesian Monte Carlo, a principled method of approximate integration. We employ the error bars of our GP's predictions as a means to select only the most informative data to store. This allows us to introduce an iterative formulation of the GP to give a dynamic, on-line algorithm. We also show how our error bars can be used to perform active data selection, allowing the GP to select where and when it should next take a measurement. We demonstrate how our methods can be applied to multi-sensor prediction problems where data may be missing, delayed and/or correlated. In particular, we present a real network of weather sensors as a testbed for our algorithm.