Symmetry Exploits for Bayesian Cubature Methods

Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited. This additional flexibility, compared to many classical cubature methods, comes at a computational cost which is cubic in the number of evaluations of...

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Published in:arXiv.org 2019-01
Main Authors: Karvonen, Toni, Särkkä, Simo, Oates, Chris J
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Language:English
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Bayesian analysis
Coding
Computational efficiency
Numerical integration
Pricing policies
Symmetry
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Särkkä, Simo
Oates, Chris J
description Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited. This additional flexibility, compared to many classical cubature methods, comes at a computational cost which is cubic in the number of evaluations of the integrand. It has been recently observed that fully symmetric point sets can be exploited in order to reduce - in some cases substantially - the computational cost of the standard Bayesian cubature method. This work identifies several additional symmetry exploits within the Bayesian cubature framework. In particular, we go beyond earlier work in considering non-symmetric measures and, in addition to the standard Bayesian cubature method, present exploits for the Bayes-Sard cubature method and the multi-output Bayesian cubature method.
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subjects Bayesian analysis
Coding
Computational efficiency
Numerical integration
Pricing policies
Symmetry
title Symmetry Exploits for Bayesian Cubature Methods
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