Bayesian Quadrature for Ratios
Abstract
We describe a novel approach to quadrature for ratios of probabilistic integrals, such as are used to compute posterior probabilities. It offers performance superior to Monte Carlo methods by exploiting a Bayesian quadrature framework. We improve upon previous Bayesian quadrature techniques by explicitly modelling the non-negativity of our integrands, and the correlations that exist between them. It offers most where the integrand is multi-modal and expensive to evaluate, as is commonplace in exoplanets research; we demonstrate the efficacy of our method on data from the Kepler spacecraft.
Cite
Text
Osborne et al. "Bayesian Quadrature for Ratios." Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, 2012.Markdown
[Osborne et al. "Bayesian Quadrature for Ratios." Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, 2012.](https://mlanthology.org/aistats/2012/osborne2012aistats-bayesian/)BibTeX
@inproceedings{osborne2012aistats-bayesian,
title = {{Bayesian Quadrature for Ratios}},
author = {Osborne, Michael and Garnett, Roman and Roberts, Stephen and Hart, Christopher and Aigrain, Suzanne and Gibson, Neale},
booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics},
year = {2012},
pages = {832-840},
volume = {22},
url = {https://mlanthology.org/aistats/2012/osborne2012aistats-bayesian/}
}