vecchia_profbeta_loglik_grad_info | R Documentation |
This function returns Vecchia's (1988) approximation to the Gaussian loglikelihood, profiling out the regression coefficients, and returning the gradient and Fisher information. Vecchia's 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_grad_info(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
grad
: gradient with respect to covariance parameters
info
: Fisher information for covariance parameters
betahat
: profile likelihood estimate of regression coefs
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_grad_info( covparms, "matern_isotropic",
# y, X, locs, NNarray )
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