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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]
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 ...
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 .
This method uses Gaussian process regression (GPR) to fit a probabilistic model from which replicates may then be drawn. GPR is a Bayesian non-linear regression method. A Gaussian process (GP) is a collection of random variables, any finite number of which have a joint Gaussian (normal) distribution.
The second is based on quantile regression using values of the process which are close to the value one is trying to predict, where distance is measured in terms of a metric on the set of indices. Local Approximate Gaussian Process uses a similar logic but constructs a valid stochastic process based on these neighboring values.
In Gaussian process regression, also known as Kriging, a Gaussian prior is assumed for the regression curve. The errors are assumed to have a multivariate normal distribution and the regression curve is estimated by its posterior mode. The Gaussian prior may depend on unknown hyperparameters, which are usually estimated via empirical Bayes. The ...
A more general class of regression-based multi-fidelity methods are Bayesian approaches, e.g. Bayesian linear regression, [3] Gaussian mixture models, [10] [11] Gaussian processes, [12] auto-regressive Gaussian processes, [2] or Bayesian polynomial chaos expansions.
A non-trivial way to mix the latent functions is by convolving a base process with a smoothing kernel. If the base process is a Gaussian process, the convolved process is Gaussian as well. We can therefore exploit convolutions to construct covariance functions. [20] This method of producing non-separable kernels is known as process convolution.