dot-cor_fs: Calculate correlation for fully symmetric model

In mcgf: Markov Chain Gaussian Fields Simulation and Parameter Estimation

Calculate correlation for fully symmetric model

Description

Calculate correlation for fully symmetric model

Usage

.cor_fs(nugget, c, gamma = 1/2, a, alpha, beta = 0, h, u)

Arguments

nugget	The nugget effect \in[0, 1].
c	Scale parameter of cor_exp, c>0.
gamma	Smooth parameter of cor_exp, \gamma\in(0, 1/2].
a	Scale parameter of cor_cauchy, a>0.
alpha	Smooth parameter of cor_cauchy, \alpha\in(0, 1].
beta	Interaction parameter, \beta\in[0, 1].
h	Euclidean distance matrix or array.
u	Time lag, same dimension as h.

Details

The fully symmetric correlation function with interaction parameter \beta has the form

C(\mathbf{h}, u)=\dfrac{1}{(a|u|^{2\alpha} + 1)} \left((1-\text{nugget})\exp\left(\dfrac{-c\|\mathbf{h}\|^{2\gamma}} {(a|u|^{2\alpha}+1)^{\beta\gamma}}\right)+ \text{nugget}\cdot \delta_{\mathbf{h}=\boldsymbol 0}\right),

where \|\cdot\| is the Euclidean distance, and \delta_{x=0} is 1 when x=0 and 0 otherwise. Here \mathbf{h}\in\mathbb{R}^2 and u\in\mathbb{R}. By default beta = 0 and it reduces to the separable model.

Value

Correlations of the same dimension as h and u.

References

Gneiting, T. (2002). Nonseparable, Stationary Covariance Functions for Space–Time Data, Journal of the American Statistical Association, 97:458, 590-600.

mcgf documentation built on June 29, 2024, 9:09 a.m.