Bayesian Quadrature for Ratios

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 data from the Kepler space telescope.

• Type: Journal
• Year: 2012
• Where: JMLR
• Authors: Michael A. Osborne, Roman Garnett, Stephen J. Roberts, Christopher Hart, Suzanne Aigrain, Neale Gibson
• Keywords: Cacy, Integrand, JMLR 2012, Programming Languages, Space Telescope