A Gaussian process is a stochastic process Xt, t ∈ T, for which any finite linear combination of samples has a joint Gaussian distribution. More accurately, any linear functional applied to the sample function Xt will give a normally distributed result. Notation-wise, one can write X ∼ GP(m, K), meaning: the random function X "is distributed as a GP with mean function m and covariance function K". When the input vector t is two- or multi-dimensional a Gaussian process might be also known as a Gaussian random field.
Some authors assume the random variables Xt have mean zero; this greatly simplifies calculations without loss of generality and allows the mean square properties of the process to be entirely determined by the covariance function K.
Read more about Gaussian Process: Alternative Definitions, Covariance Functions, Important Gaussian Processes, Applications
Famous quotes containing the word process:
“If thinking is like perceiving, it must be either a process in which the soul is acted upon by what is capable of being thought, or a process different from but analogous to that. The thinking part of the soul must therefore be, while impassable, capable of receiving the form of an object; that is, must be potentially identical in character with its object without being the object. Mind must be related to what is thinkable, as sense is to what is sensible.”
—Aristotle (384–322 B.C.)