vecchia_grouped_profbeta_loglik_grad_info: Grouped Vecchia loglikelihood, gradient, Fisher information
In GpGp: Fast Gaussian Process Computation Using Vecchia's Approximation

Description Usage Arguments Value Examples

This function returns a grouped version (Guinness, 2018) of Vecchia's (1988) approximation to the Gaussian loglikelihood, the gradient, and Fisher information, and the profile likelihood estimate of 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_grouped_profbeta_loglik_grad_info(
  covparms,
  covfun_name,
  y,
  X,
  locs,
  NNlist
)

`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
`X`	Design matrix of covariates. Row `i` of `X` contains the covariates for the observation at row `i` of `locs`.
`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`.
`NNlist`	A neighbor list object, the output from `group_obs`.

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 <- fast_Gp_sim(covparms, "matern_isotropic", locs, 50 )
ord <- order_maxmin(locs)
NNarray <- find_ordered_nn(locs,20)
NNlist <- group_obs(NNarray)
#loglik <- vecchia_grouped_profbeta_loglik_grad_info( 
#    covparms, "matern_isotropic", y, X, locs, NNlist )