nsgpModel {BayesNSGP}

NIMBLE code for a generic nonstationary GP model

Description

This function sets up and compiles a nimble model for a general nonstationary Gaussian process.

Usage

nsgpModel(
  tau_model = "constant",
  sigma_model = "constant",
  Sigma_model = "constant",
  mu_model = "constant",
  likelihood = "fullGP",
  coords,
  data,
  constants = list(),
  monitorAllSampledNodes = TRUE,
  ...
)

Arguments

tau_model

Character; specifies the model to be used for the log(tau) process. Options are "constant" (spatially-constant), "logLinReg" (log-linear regression), and "approxGP" (approximation to a Gaussian process).

sigma_model

Character; specifies the model to be used for the log(sigma) process. See tau_model for options.

Sigma_model

Character; specifies the model to be used for the Sigma anisotropy process. Options are "constant" (spatially-constant), "constantIso" (spatially-constant and isotropic), "covReg" (covariance regression), "compReg" (componentwise regression), "compRegIso" (isotropic componentwise regression), "npApproxGP" (nonparameteric regression via an approximation to a stationary Gaussian process), and "npApproxGPIso" (isotropic nonparameteric regression via an approximation to a stationary Gaussian process)

mu_model

Character; specifies the model to be used for the mu mean process. Options are "constant" (spatially-constant), "linReg" (linear regression), and "zero" (a fixed zero-mean).

likelihood

Character; specifies the likelihood model. Options are "fullGP" (the exact Gaussian process likelihood), "NNGP" (the nearest-neighbor GP for the response approximate likelihood), and "SGV" (the sparse general Vecchia approximate likelihood).

coords

N x d matrix of spatial coordinates.

data

N-vector; observed vector of the spatial process of interest

constants

A list of constants required to build the model; depends on the specific parameter process models chosen.

monitorAllSampledNodes

Logical; indicates whether all sampled nodes should be stored (TRUE) or not (FALSE).

...

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

A nimbleCode object.

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 )