Specify a multivariate Vecchia approximation

Specifies a multivariate Vecchia approximation for later use in likelihood evaluation or prediction. This function does not depend on parameter values, and only has to be run once before repeated likelihood evaluations. This function is a multivariate version of vecchia_specify.

Usage

vecchia_Mspecify(
  locs.list,
  m,
  locs.list.pred = NULL,
  dist.func = NULL,
  ordering.pred = c("obspred", "general"),
  pred.cond = c("independent", "general")
)

Arguments

locs.list

List of observed locations. Each each element should be a matrix containing the locs for the corresponding outcome variable.

m

Number of nearby points to condition on.

locs.list.pred

List of locations at which to make predictions. Each element should be a matrix containing the locs for the corresponding outcome variable.

dist.func

Any distance function with a signature of dist(query_location, locations_matrix). Defaults to Euclidean distance.

ordering.pred

Should "obspred" or "general" ordering be used for prediction? See vecchia_specify. Defaults to "obspred".

pred.cond

Should prediction conditioning be "general" or "independent"? See vecchia_specify. Defaults to "independent".

Value

An object that specifies the multivariate Vecchia approximation for later use in likelihood evaluation or prediction.

Details

This function should produce identical results to vecchia_specify for univariate problems, although it has fewer options. We recommend that vecchia_specify be used in the univariate case.

References

• Katzfuss, M., and Guinness, J. "A general framework for Vecchia approximations of Gaussian processes", Statistical Science (2021) 36(1):124-141.

See also

vecchia_specify

Examples

data(soil)
soil <- soil[!is.na(soil[,5]),] # remove rows with NA's
locs <- as.matrix(soil[,1:2])
locsm <- list()
locsm[[1]] <- locsm[[2]] <- locs
soil.va <- vecchia_Mspecify(locsm, m=10)