Speaker
Description
The formalism of Bayesian model selection provides a very 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. This usually necessitates a large number of function calls to the likelihood, which may become prohibitive in case of ``slow'', costly to evaluate likelihoods. A possible solution to this problem lies in approximating the slow full likelihood by a fast emulated likelihood. I will present BOBE (Bayesian Optimisation for Bayesian Evidence), a method to construct a Gaussian Process Regression (GPR)-based emulator. BOBE utilises a Bayesian Optimisation algorithm designed specifically to (i) provide a realistic estimate of the emulator's uncertainty and its impact on the evidence calculation, and (ii) minimise the number of likelihood evaluations required in order to meet a given evidence accuracy goal. I will show, through application to toy models as well as actual cosmological likelihoods, that training the emulator to a sufficient accuracy takes a factor of $\mathcal{O}(10^3)$ fewer direct likelihood evaluations than would be needed if one were to directly compute the evidence integral via nested sampling.