Bayesian Numerical Integration Algorithm: Difference between revisions
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A [[Bayesian Numerical Integration Algorithm]] is a [[ | A [[Bayesian Numerical Integration Algorithm]] is a [[integral estimation algorithm]] that [[Gaussian Process]] that ... | ||
* <B>AKA:</B> [[Bayesian Quadrature]]. | * <B>AKA:</B> [[Bayesian Numerical Integration Algorithm|Bayesian Quadrature]]. | ||
* <B>Context:</B> | * <B>Context:</B> | ||
** It can provide a full handling of the uncertainty over the solution of the integral expressed as a [[Gaussian Process]] [[posterior variance]]. | ** It can provide a full handling of the uncertainty over the solution of the integral expressed as a [[Gaussian Process]] [[posterior variance]]. | ||
* <B>See:</B> [[Gaussian Process]]. | * <B>See:</B> [[Gaussian Process]]. | ||
---- | ---- | ||
---- | ---- | ||
==References== | |||
== References == | |||
=== 2017 === | === 2017 === | ||
* (Wikipedia, 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. | ** 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 === | === 1991 === | ||
* ([[Hagan, 1991]]) ⇒ [[Anthony O'Hagan]]. ([[1991]]). “Bayes–Hermite Quadrature.” In: Journal of Statistical Planning and Inference 29(3). [https://doi.org/10.1016/0378-3758(91)90002-V doi:10.1016/0378-3758(91)90002-V] | * ([[Hagan, 1991]]) ⇒ [[Anthony O'Hagan]]. ([[1991]]). “Bayes–Hermite Quadrature.” In: Journal of Statistical Planning and Inference 29(3). [https://doi.org/10.1016/0378-3758(91)90002-V doi:10.1016/0378-3758(91)90002-V] | ||
** ABSTRACT: [[Bayesian quadrature]] treats the [[problem of numerical integration]] as one of [[statistical inference]]. </s> A [[prior distribution|prior]] [[Gaussian process distribution]] is assumed for the [[integrand]], observations arise from [[evaluating the integrand]] at selected [[point]]s, and a [[posterior distribution]] is derived for the [[integrand]] and the [[integral]]. </s> [[quadrature method|Method]]s are developed for [[quadrature]] in p. </s> A particular [[application]] is [[integrating the posterior density]] arising from some other [[Bayesian analysis]]. </s> | ** ABSTRACT: [[Bayesian Numerical Integration Algorithm|Bayesian quadrature]] treats the [[problem of numerical integration]] as one of [[statistical inference]]. </s> A [[prior distribution|prior]] [[Gaussian process distribution]] is assumed for the [[integrand]], observations arise from [[evaluating the integrand]] at selected [[point]]s, and a [[posterior distribution]] is derived for the [[integrand]] and the [[integral]]. </s> [[quadrature method|Method]]s are developed for [[quadrature]] in p. </s> A particular [[application]] is [[integrating the posterior density]] arising from some other [[Bayesian analysis]]. </s> | ||
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[[Category:Concept]] | [[Category:Concept]] | ||
Latest revision as of 22:09, 16 June 2021
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.
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.