Evaluation of the multivariate Vecchia likelihood

This function is used to evaluate the multivariate Vecchia likelihood.

Usage

vecchia_Mlikelihood(z, vecchia.approx, covparams)

Arguments

z

The observed data.

vecchia.approx

A Vecchia object returned by vecchia_Mspecify.

covparams

Vector of covariance parameters. See create.param.sequence or the examples below for details about the format of this vector.

Value

The log likelihood implied by the multivariate Vecchia approximation.

References

• Katzfuss, M., and Guinness, J. "A general framework for Vecchia approximations of Gaussian processes", Statistical Science (2021) 36(1):124-141.

See also

vecchia_likelihood, vecchia_Mspecify, create.param.sequence

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

vecchia_Mlikelihood(rnorm(nrow(locs)), soil.va, params)
#> [1] NA