dot-cor_stat: Calculate general stationary correlation.

In mcgf: Markov Chain Gaussian Fields Simulation and Parameter Estimation

Calculate general stationary correlation.

Description

Calculate general stationary correlation.

Usage

.cor_stat(base, lagrangian, par_base, par_lagr, lambda, base_fixed = FALSE)

Arguments

base	Base model, sep or fs for now. Or correlation matrix/array.
lagrangian	Lagrangian model, none, lagr_tri, or lagr_askey.
par_base	Parameters for the base model (symmetric), used only when base_fixed = FALSE.
par_lagr	Parameters for the Lagrangian model. Used only when lagrangian is not none.
lambda	Weight of the Lagrangian term, \lambda\in[0, 1].
base_fixed	Logical; if TRUE, base is the correlation.

Details

The general station model, a convex combination of a base model and a Lagrangian model, has the form

C(\mathbf{h}, u)=(1-\lambda)C_{\text{Base}}(\mathbf{h}, u)+ \lambda C_{\text{Lagr}}(\mathbf{h}, u),

where \lambda is the weight of the Lagrangian term.

If base_fixed = TRUE, the correlation is of the form

C(\mathbf{h}, u)=(1-\lambda)C_{\text{Base}}+ \lambda C_{\text{Lagr}}(\mathbf{h}, u),

where base is a correlation matrix/array and par_base and h are not used.

When lagrangian = "none", lambda must be 0.

Value

Correlations for the general stationary model. Same dimension of base if base_fixed = FALSE.

References

Gneiting, T., Genton, M., & Guttorp, P. (2006). Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry. In C&H/CRC Monographs on Statistics & Applied Probability (pp. 151–175). Chapman and Hall/CRC.

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