ss {multivator}

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)

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.

Value

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

Note

Thanks to Stephen Stretton for a crucial insight here

Author(s)

Robin K. S. Hankin

Examples

data(mtoys)
ss_matrix(toy_mhp)