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Multivariate Vecchia prediction

vecchia_Mprediction.Rd

This function is used to make predictions based on multivariate Vecchia models. It is a multivariate version of vecchia_prediction.

Usage

vecchia_Mprediction(
  z,
  vecchia.approx,
  covparms,
  var.exact = NULL,
  return.values = "mean"
)

Arguments

z

The observed data.

vecchia.approx

A Vecchia object returned by vecchia_Mspecify.

covparms

Vector of covariance parameters. See create.param.sequence or the examples below for details about the format of this vector.

var.exact

Should prediction variances by computed exactly, or is a (faster) approximation acceptable? See vecchia_prediction.

return.values

Values that should be returned. Possible values include "mean", "meanvar", "meanmat", and "all". See vecchia_prediction. Defaults to "mean".

Value

The posterior means/variances/V matrices at the observed and unobserved locations. See vecchia_prediction.

References

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

  • Katzfuss, M., Guinness, J., Gong, W. and Zilber, D. "Vecchia approximations of Gaussian-process predictions", Journal of Agricultural, Biological and Environmental Statistics (2020) 25:383-414.

See also

vecchia_prediction, vecchia_Mspecify, create.param.sequence

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
locsp <- locsm
locsp[[1]] <- locsp[[1]] + 0.5
locsp[[2]] <- locsp[[2]] - 0.5
soil.vap <- vecchia_Mspecify(locsm, m=10, locs.list.pred=locsp)

pseq <- create.param.sequence(2)
# Initialize the vector of covariance parameters
params <- rep(NA, pseq[5,2])
# Sigma parameters:
params[pseq[1,1]:pseq[1,2]] <- c(100, 80)
# Scale parameters:
params[pseq[2,1]:pseq[2,2]] <- c(60, 50)
# Smoothness parameters:
params[pseq[3,1]:pseq[3,2]] <- c(0.5, 0.5)
# Nuggets:
params[pseq[4,1]:pseq[4,2]] <- c(30, 30)
# Correlation:
params[pseq[5,1]:pseq[5,2]] <- -0.9

soil.yhat <- vecchia_Mprediction(rnorm(nrow(locs)), soil.vap, params)