Bayesian Numerical Integration Algorithm

A Bayesian Numerical Integration Algorithm is a integral estimation algorithm that Gaussian Process that ...

• AKA: Bayesian Quadrature.
• Context:
  • It can provide a full handling of the uncertainty over the solution of the integral expressed as a Gaussian Process posterior variance.
• See: Gaussian Process.

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References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Numerical_integration#Bayesian_Quadrature Retrieved:2017-9-16.
  • Bayesian Quadrature is a statistical approach to the numerical problem of computing integrals and falls under the field of probabilistic numerics. It can provide a full handling of the uncertainty over the solution of the integral expressed as a Gaussian Process posterior variance. It is also known to provide very fast convergence rates which can be up to exponential in the number of quadrature points n.

1991

• (Hagan, 1991) ⇒ Anthony O'Hagan. (1991). “Bayes–Hermite Quadrature.” In: Journal of Statistical Planning and Inference 29(3). doi:10.1016/0378-3758(91)90002-V
  • ABSTRACT: Bayesian quadrature treats the problem of numerical integration as one of statistical inference. A prior Gaussian process distribution is assumed for the integrand, observations arise from evaluating the integrand at selected points, and a posterior distribution is derived for the integrand and the integral. Methods are developed for quadrature in p. A particular application is integrating the posterior density arising from some other Bayesian analysis.

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