Description Usage Arguments Value Examples

Definition of the Matern Covariance function, if *2 ν* is integer. For
*ν =* `0.5`

the function is also known as the exponential covariance or the
Ornstein-Uhlenbeck covariance in one dimension. In general the explicit formula
for the Matern Covariance for one dimensional processes, with *ν* s.t. *ν = p + 0.5* and *p* integer is:

*
k(d) = s^2 \frac{p!}{(2p)!} exp≤ft(-\frac{√{2 ν} d}{ρ}\right) ∑_{i = 0}^p \frac{(p+i)!}{(p-i)! i!} ≤ft( \frac{√{8 ν} d}{ρ} \right)^{p-i}
*

with *d* the distance between two points *x* and *y* in R.

1 | ```
covMaterniso(nu, rho, sigma, x)
``` |

`nu` |
scalar. Value s.t. 2 |

`rho` |
scalar. Non negative range parameter |

`sigma` |
scalar. Non negative standard deviation parameter |

`x` |
vector. Vector containing the abscissa points where the Covariance is defined. |

`d`

*\times*`d`

covariance matrix.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
# Defintion of a Gaussian process
# with Matern Covariance
# Time domain of the Gaussian Process
M <- 50
T_domain <- seq(0, 1, length = M)
# paramteters of the Matern Covariance
nu_alpha <- 2.5
range <- 1/4
variance <- 1
# mean of the process
mu_alpha <- rep(0,M)
# covariance structure
Sig_alpha <- covMaterniso(nu_alpha, rho = range, sigma = sqrt(variance), T_domain)
# definition of the process
# alpha <- mvrnorm(mu=mu_alpha, Sigma=Sig_alpha, n=1) # if MASS is inslalled
``` |

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