Bayesian Quadrature for Ratios: Now With Even More Bayesian Quadrature

We describe a novel approach to quadrature for ratios of probabilistic integrals, such as are used to compute posterior probabilities. This approach offers performance superior to Monte Carlo methods by exploiting a Bayesian quadrature framework. We improve upon previous Bayesian quadrature techniques by explicitly modelling the nonnegativity of our integrands, and the correlations that exist between them. It offers most where the integrand is multi-modal and expensive to evaluate. We demonstrate the efficacy of our method on complex exoplanet data from the Kepler space telescope. Abstract We describe a novel approach to quadrature for ratios of probabilistic integrals, such as are used to compute posterior probabilities. This approach offers performance superior to Monte Carlo methods by exploiting a Bayesian quadrature framework. We improve upon previous Bayesian quadrature techniques by explicitly modelling the nonnegativity of our integrands, and the correlations that exist between them. It offers most Appearing in Proceedings of the 15 International Conference on Artificial Intelligence and Statistics (AISTATS) 2012, La Palma, Canary Islands. Volume 22 of JMLR: W&CP 22. Copyright 2012 by the authors. where the integrand is multi-modal and expensive to evaluate. We demonstrate the efficacy of our method on complex exoplanet data from the Kepler space telescope.