nsgpPredict {BayesNSGP}

Posterior prediction for the NSGP

Description

nsgpPredict conducts posterior prediction for MCMC samples generated using nimble and nsgpModel.

Usage

nsgpPredict(
  model,
  samples,
  coords.predict,
  predict.process = TRUE,
  constants,
  seed = 0,
  ...
)

Arguments

model

A NSGP nimble object; the output of nsgpModel.

samples

A matrix of J rows, each is an MCMC sample of the parameters corresponding to the specification in nsgpModel.

coords.predict

M x d matrix of prediction coordinates.

predict.process

Logical; determines whether the prediction corresponds to the y(·) process (TRUE) or z(·) (FALSE; this would likely only be used for, e.g., cross-validation).

constants

An optional list of contants to use for prediction; alternatively, additional arguments can be passed to the function via the ... argument.

seed

An optional random seed argument for reproducibility.

...

Additional arguments can be passed to the function; for example, as an alternative to the constants list, items can be passed directly via this argument.

Value

The output of the function is a list with two elements: obs, a matrix of J posterior predictive samples for the N observed locations (only for likelihood = "SGV", which produces predictions for the observed locations by default; this element is NULL otherwise); and pred, a corresponding matrix of posterior predictive samples for the prediction locations. Ordering and neighbor selection for the prediction coordinates in the SGV likelihood are conducted internally, as with nsgpModel.

Examples

# Generate some data: stationary/isotropic
N <- 100
coords <- matrix(runif(2*N), ncol = 2)
alpha_vec <- rep(log(sqrt(1)), N) # Log process SD
delta_vec <- rep(log(sqrt(0.05)), N) # Log nugget SD
Sigma11_vec <- rep(0.4, N) # Kernel matrix element 1,1
Sigma22_vec <- rep(0.4, N) # Kernel matrix element 2,2
Sigma12_vec <- rep(0, N) # Kernel matrix element 1,2
mu_vec <- rep(0, N) # Mean
nu <- 0.5 # Smoothness
dist_list <- nsDist(coords)
Cor_mat <- nsCorr( dist1_sq = dist_list$dist1_sq, dist2_sq = dist_list$dist2_sq, 
                   dist12 = dist_list$dist12, Sigma11 = Sigma11_vec, 
                   Sigma22 = Sigma22_vec, Sigma12 = Sigma12_vec, nu = nu )
Cov_mat <- diag(exp(alpha_vec)) %*% Cor_mat %*% diag(exp(alpha_vec))
D_mat <- diag(exp(delta_vec)^2) 
set.seed(110)
data <- as.numeric(mu_vec + t(chol(Cov_mat + D_mat)) %*% rnorm(N))
# Set up constants
constants <- list( nu = 0.5, Sigma_HP1 = 2 )
# Defaults: tau_model = "constant", sigma_model = "constant", mu_model = "constant",
# and Sigma_model = "constant"
Rmodel <- nsgpModel(likelihood = "fullGP", constants = constants, coords = coords, data = data )
conf <- configureMCMC(Rmodel)
Rmcmc <- buildMCMC(conf)
Cmodel <- compileNimble(Rmodel)
Cmcmc <- compileNimble(Rmcmc, project = Rmodel)
samples <- runMCMC(Cmcmc, niter = 200, nburnin = 100)
# Prediction
predCoords <- as.matrix(expand.grid(seq(0,1,l=10),seq(0,1,l=10)))
postpred <- nsgpPredict( model = Rmodel, samples = samples, coords.predict = predCoords )