makeCov: Construct full (bivariate) covariance/precision matrix

In andrewzm/bicon: Bivariate modelling using the conditional approach

Description

Construct the covariance or precision matrix for the bivariate model constructed using the conditional approach.

Usage

makeSY(r, var1, var2, kappa1, kappa2, B, nu1 = 3/2, nu2 = 3/2)

makeQY(r, var1, var2, kappa1, kappa2, B, nu1 = 3/2, nu2 = 3/2)

makeQ(r, var, kappa, nu)

makeS(r, var, kappa, nu)

Arguments

r	vector of distances
var1	variance of C_11
var2	variance of C_2|1
kappa1	scale of C_11
kappa2	scale of C_2|1
B	interaction matrix
var	variance of C
kappa	scale of C

Details

Both C_11 and C_2|1 are Matern covariance functions with smoothness parameter equal to 3/2. Covariance matrices are computed from Matern covariance functions using the vector of distances r, so that Sigma[1,1] = cov(Y1(s),Y1(s+r[1])), Sigma[1 + n,1] = cov(Y2(s),Y1(s+r[1])) and so on. Currently the grids on which Y1 and Y2 are evaluated need to be identical.

The matrix B is the interaction matrix. The full covariance matrix returned is

Sigma = [Sigma_{11} & Sigma_{11}B' ; B Sigma_{11} & Sigma_{2|1} + B Sigma_{11}B'].

Value

Covariance (or precision) matrix

Examples

s <- 0 : 99
D <- as.matrix(dist(s))
r <- as.vector(D)

## Assume the interaction matrix is the identity
B <- diag(100)
Sigma <- makeSY(r=r,var1=1,var2=1,kappa1=0.5,kappa2=0.1,B=B)
image(Sigma)

andrewzm/bicon documentation built on May 10, 2019, 11:15 a.m.