vecchia_meanzero_loglik {GpGp}

Vecchia's approximation to the Gaussian loglikelihood, zero mean

Description

This function returns Vecchia's (1988) approximation to the Gaussian loglikelihood. The approximation modifies the ordered conditional specification of the joint density; rather than each term in the product conditioning on all previous observations, each term conditions on a small subset of previous observations.

Usage

vecchia_meanzero_loglik(covparms, covfun_name, y, locs, NNarray)

Arguments

covparms

A vector of covariance parameters appropriate for the specified covariance function

covfun_name

See GpGp for information about covariance functions.

y

vector of response values

locs

matrix of locations. Row i of locs specifies the location of element i of y, and so the length of y should equal the number of rows of locs.

NNarray

A matrix of indices, usually the output from find_ordered_nn. Row i contains the indices of the observations that observation i conditions on. By convention, the first element of row i is i.

Value

a list containing

• loglik: the loglikelihood

Examples

n1 <- 20
n2 <- 20
n <- n1*n2
locs <- as.matrix( expand.grid( (1:n1)/n1, (1:n2)/n2 ) )
covparms <- c(2, 0.2, 0.75, 0)
y <- fast_Gp_sim(covparms, "matern_isotropic", locs, 50 )
ord <- order_maxmin(locs)
NNarray <- find_ordered_nn(locs,20)
#loglik <- vecchia_meanzero_loglik( covparms, "matern_isotropic", y, locs, NNarray )