# covMaterniso: Compute the Covariance of a Matern process In ardeeshany/FLAME: FLAME for high-dimensional Function-on-Scalar regression problems

## Description

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.

## Usage

 1 covMaterniso(nu, rho, sigma, x) 

## Arguments

 nu scalar. Value s.t. 2nu is integer. It is a smoothing paramter ν of the covariance: the larger nu, the smoother the process. rho scalar. Non negative range parameter ρ of the covariance. sigma scalar. Non negative standard deviation parameter s of the covariance. x vector. Vector containing the abscissa points where the Covariance is defined.

## Value

d \timesd covariance matrix.

## Examples

  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 

ardeeshany/FLAME documentation built on Sept. 25, 2017, 9:55 a.m.