vecchia_profbeta_loglik | R Documentation |
This function returns Vecchia's (1988) approximation to the Gaussian loglikelihood, profiling out the regression coefficients. 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.
vecchia_profbeta_loglik(covparms, covfun_name, y, X, locs, NNarray)
covparms |
A vector of covariance parameters appropriate for the specified covariance function |
covfun_name |
See |
y |
vector of response values |
X |
Design matrix of covariates. Row |
locs |
matrix of locations. Row |
NNarray |
A matrix of indices, usually the output from |
a list containing
loglik
: the loglikelihood
betahat
: profile likelihood estimate of regression coefficients
betainfo
: information matrix for betahat
.
The covariance
matrix for $betahat
is the inverse of $betainfo
.
n1 <- 20
n2 <- 20
n <- n1*n2
locs <- as.matrix( expand.grid( (1:n1)/n1, (1:n2)/n2 ) )
X <- cbind(rep(1,n),locs[,2])
covparms <- c(2, 0.2, 0.75, 0)
y <- X %*% c(1,2) + fast_Gp_sim(covparms, "matern_isotropic", locs, 50 )
ord <- order_maxmin(locs)
NNarray <- find_ordered_nn(locs,20)
#loglik <- vecchia_profbeta_loglik( covparms, "matern_isotropic", y, X, locs, NNarray )
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