Bayesian Numerical Integration Algorithm: Difference between revisions

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A [[Bayesian Numerical Integration Algorithm]] is a [[numerical integration algorithm]] that [[Gaussian Process]] that ...
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]].
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==References==
 
== References ==


=== 2017 ===
=== 2017 ===
* (Wikipedia, 2017) &rArr; https://en.wikipedia.org/wiki/Numerical_integration#Bayesian_Quadrature Retrieved:2017-9-16.
* (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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Latest revision as of 22:09, 16 June 2021

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



References

2017

1991