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Inference of continuous values with a Gaussian process prior is known as Gaussian process regression, or kriging; extending Gaussian process regression to multiple target variables is known as cokriging. [26] Gaussian processes are thus useful as a powerful non-linear multivariate interpolation tool. Kriging is also used to extend Gaussian ...
A Neural Network Gaussian Process (NNGP) is a Gaussian process (GP) obtained as the limit of a certain type of sequence of neural networks. Specifically, a wide variety of network architectures converges to a GP in the infinitely wide limit , in the sense of distribution .
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.
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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 .
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.
Bayesian optimization of a function (black) with Gaussian processes (purple). Three acquisition functions (blue) are shown at the bottom. [8]Bayesian optimization is typically used on problems of the form (), where is a set of points, , which rely upon less (or equal to) than 20 dimensions (,), and whose membership can easily be evaluated.
The increment process X(t) is known as fractional Gaussian noise. There is also a generalization of fractional Brownian motion: n -th order fractional Brownian motion , abbreviated as n-fBm. [ 1 ] n-fBm is a Gaussian , self-similar, non-stationary process whose increments of order n are stationary.