**Michael Osborne**

Wednesday 1st May 2013

**Time: 4pm**

** **

Basement Seminar Room

Alexandra House, 17 Queen Square, London, WC1N 3AR

** Bayesian Quadrature for Prediction and Optimisation**

Numerical integration is an key component of many
problems in scientiﬁc computing, statistical modelling, and machine learning. Bayesian Quadrature is a model-based method for numerical integration which, relative to standard Monte Carlo methods, offers increased sample efﬁciency and a more robust estimate of the uncertainty in the estimated integral. We propose a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model. Our approach approximately marginalises the quadrature model’s hyperparameters in closed form, and introduces an active learning scheme to optimally select function evaluations, as opposed to using Monte Carlo samples. We then present results of the use of Bayesian quadrature for problems related to changepoint and fault detection, global optimisation and real scientiﬁc problems from astronomy.