# vecchia_grouped_profbeta_loglik: Grouped Vecchia approximation, profiled regression... In GpGp: Fast Gaussian Process Computation Using Vecchia's Approximation

## Description

This function returns a grouped version (Guinness, 2018) of Vecchia's (1988) approximation to the Gaussian loglikelihood 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.

## Usage

 `1` ```vecchia_grouped_profbeta_loglik(covparms, covfun_name, y, X, locs, NNlist) ```

## 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 `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`.

## Value

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`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```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( # covparms, "matern_isotropic", y, X, locs, NNlist ) ```

GpGp documentation built on June 10, 2021, 1:07 a.m.