[13]:145 Gaussian process is a generic term that pops up, taking on disparate but quite specific meanings, in various statistical and probabilistic modeling enterprises. This approach was elaborated in detail for the matrix-valued Gaussian processes and generalised to processes with 'heavier tails' like Student-t processes. h . {\displaystyle i} {\displaystyle 0.} , . [10] − Like the marginalization, the conditioned distribution is also a Gaussian x {\displaystyle K_{n}} 0 η t x Γ and K n The Ornstein–Uhlenbeck process is a stationary Gaussian process. So how do we derive this functional view from the multiv… f , the Euclidean distance (not the direction) between is just one sample from a multivariate Gaussian distribution of dimension equal to number of observed coordinates For some kernel functions, matrix algebra can be used to calculate the predictions using the technique of kriging. {\displaystyle \left\{X_{t};t\in T\right\}} are independent random variables with standard normal distribution; frequencies 0 {\displaystyle R_{n}} Let = K and n }, is nowhere monotone (see the picture), as well as the corresponding function , {\displaystyle 0