A Gaussian process (GP) is a generalization of the Gaussian probability distribution.
Generalists assign a prior probability to functions.
The specification of the prior is important, because it fixes the properties of the functions considered for inference.
The properties of a GP are induced by the covariance function of the process.
A Gaussian process is a stochastic process either a collection of random variables with a temporal or spatial index such that each finite collection of these random variables follows a multidimensional normal law, each linear combination is normally distributed.
The distribution of a Gaussian process is the joint distribution of all these random variables.
Its realizations are therefore functions with a continuous domain.
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