Create the sparse triangular matrix U for multivariate Vecchia models

This creates the sparse triangular matrix U for multivariate Vecchia models. This matrix can be used to estimate the likelihood or transform the data to be iid. This function is a multivariate version of createU.

Usage

createUMultivariate(vec_approx, params)

Arguments

vec_approx: Object returned by vecchia_Mspecify.
params: Vector of covariance parameters. See create_param_sequence or the examples below for details about the format of this vector.

Value

A list containing the sparse upper trianguler U, plus additional objects required for other functions.

References

Apanasovich, T.V., Genton, M.G. and Sun, Y. "A valid Matérn class of cross-covariance functions for multivariate random fields with any number of components", Journal of the American Statistical Association (2012) 107(497):180-193.
Katzfuss, M., and Guinness, J. "A general framework for Vecchia approximations of Gaussian processes", Statistical Science (2021) 36(1):124-141.

Examples

data(soil)
soil <- soil[!is.na(soil[,5]),] # remove rows with NA's
locs <- as.matrix(soil[,1:2])
locsm <- list()
locsm[[1]] <- locsm[[2]] <- locs
soil.va <- vecchia_Mspecify(locsm, m=10)

pseq <- create_param_sequence(2)
# Initialize the vector of covariance parameters
params <- rep(NA, pseq[5,2])
# Sigma parameters:
params[pseq[1,1]:pseq[1,2]] <- c(100, 80)
# Scale parameters:
params[pseq[2,1]:pseq[2,2]] <- c(60, 50)
# Smoothness parameters:
params[pseq[3,1]:pseq[3,2]] <- c(0.5, 0.5)
# Nuggets:
params[pseq[4,1]:pseq[4,2]] <- c(30, 30)
# Correlation:
params[pseq[5,1]:pseq[5,2]] <- -0.9

soil.u <- createUMultivariate(soil.va, params)