Search results
Results from the WOW.Com Content Network
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 .
This model is called a Gaussian white noise signal (or process). In the mathematical field known as white noise analysis , a Gaussian white noise w {\displaystyle w} is defined as a stochastic tempered distribution, i.e. a random variable with values in the space S ′ ( R ) {\displaystyle {\mathcal {S}}'(\mathbb {R} )} of tempered distributions .
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.
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.
A one-dimensional GRF is also called a Gaussian process. An important special case of a GRF is the Gaussian free field . With regard to applications of GRFs, the initial conditions of physical cosmology generated by quantum mechanical fluctuations during cosmic inflation are thought to be a GRF with a nearly scale invariant spectrum.
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.