multivator (version 1.1-4)

ss: Overall variance matrix

Description

Calculates the maximum correlations possible consistent with the roughness parameters

Usage

ss(A, B, Ainv, Binv)
ss_matrix(hp,useM=TRUE)
ss_matrix_simple(hp,useM=TRUE)

Arguments

A,B

Positive-definite matrices (roughness parameters)

Ainv,Binv

The inverses of A and B; if missing, compute explicitly

hp

An object of class mhp

useM

Boolean, with default TRUE meaning to multiply (pointwise) by $M$ and FALSE meaning not to (so giving the maximum correlation consistent with the roughness matrices $B$)

Value

Function ss() returns a scalar, ss_matrix() a matrix of covariances.

Details

Function ss() calculates the maximum possible correlation between observations of two Gaussian processes at the same point (equation 24 of the vignette):

$$ \left| \left( \frac{1}{2}B_r+\frac{1}{2}B_s\vphantom{\frac{1}{2}B_r^{-1}} \right)\left( \frac{1}{2}B_r^{-1}+\frac{1}{2}B_s^{-1} \right) \right|^{-1/4} $$

Functions ss_matrix() and ss_matrix_simple() calculate the maximum covariances among the types of object specified in the hp argument, an object of class mhp. Function ss_matrix() is the preferred form; function ss_matrix_simple() is a less efficient, but more transparent, version. The two functions should return identical output.

Examples

data(mtoys)
ss_matrix(toy_mhp)