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Gaussian processes are also commonly used to tackle numerical analysis problems such as numerical integration, solving differential equations, or optimisation in the field of probabilistic numerics. Gaussian processes can also be used in the context of mixture of experts models, for example.
This is a comparison of statistical analysis software that allows doing inference with Gaussian processes often using approximations. This article is written from the point of view of Bayesian statistics , which may use a terminology different from the one commonly used in kriging .
A variant of Gaussian elimination called Gauss–Jordan elimination can be used for finding the inverse of a matrix, if it exists. If A is an n × n square matrix, then one can use row reduction to compute its inverse matrix, if it exists. First, the n × n identity matrix is augmented to the right of A, forming an n × 2n block matrix [A | I].
GPOPS-II [3] is designed to solve multiple-phase optimal control problems of the following mathematical form (where is the number of phases): = ((), …, ()) subject to the dynamic constraints
Vecchia approximation is a Gaussian processes approximation technique originally developed by Aldo Vecchia, a statistician at United States Geological Survey. [1] It is one of the earliest attempts to use Gaussian processes in high-dimensional settings. It has since been extensively generalized giving rise to many contemporary approximations.
In statistics, originally in geostatistics, kriging or Kriging (/ ˈ k r iː ɡ ɪ ŋ /), also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under suitable assumptions of the prior, kriging gives the best linear unbiased prediction (BLUP) at unsampled locations. [1]
Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. [1] [2] A stationary Gauss–Markov process is unique [citation needed] up to rescaling; such a process is also known as an Ornstein–Uhlenbeck process ...
In statistics and machine learning, Gaussian process approximation is a computational method that accelerates inference tasks in the context of a Gaussian process model, most commonly likelihood evaluation and prediction. Like approximations of other models, they can often be expressed as additional assumptions imposed on the model, which do ...