Editing Gaussian process (section)

{{Short description|Statistical model}}
In [[probability theory]] and [[statistics]], a '''Gaussian process''' is a [[stochastic process]] (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a [[multivariate normal distribution]]. The distribution of a Gaussian process is the [[joint distribution]] of all those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g. time or space.

The concept of Gaussian processes is named after [[Carl Friedrich Gauss]] because it is based on the notion of the Gaussian distribution ([[normal distribution]]). Gaussian processes can be seen as an infinite-dimensional generalization of multivariate normal distributions.

Gaussian processes are useful in [[statistical model]]ling, benefiting from properties inherited from the normal distribution. For example, if a [[random process]] is modelled as a Gaussian process, the distributions of various derived quantities can be obtained explicitly. Such quantities include the average value of the process over a range of times and the error in estimating the average using sample values at a small set of times. While exact models often scale poorly as the amount of data increases, multiple [[Gaussian process approximations|approximation methods]] have been developed which often retain good accuracy while drastically reducing computation time.