Speaker
Description
The formalism of Bayesian model selection provides an elegant way of ranking different physical models in terms of how compatible they are with a given set of observed data. However, its practical application is often hampered by the challenge of having to compute the Bayesian evidence - a multi-dimensional integral over the product of likelihood and prior probability which may become prohibitive in case of "slow", costly to evaluate likelihoods. We introduce a method to construct a fast Gaussian Process Regression based emulator of the likelihood using a Bayesian Optimisation algorithm designed specifically to provide a realistic estimate of the emulator's uncertainty and minimise the number of likelihood evaluations required in order to meet a given evidence accuracy goal. We discuss applications to cosmology and demonstrate using examples from the CMB that training the emulator to a sufficient accuracy takes a factor of $O(10^3)$ fewer direct likelihood evaluations compared to traditional methods such as MCMC or nested sampling. Parameter posteriors are naturally obtained as a by-product of the emulation.