# NIMBLE code for a generic nonstationary GP model This function sets up and compiles a nimble model for a general nonstationary Gaussian process. ```r nsgpModel( tau_model = "constant", sigma_model = "constant", Sigma_model = "constant", sparse_model = "none", 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) - `sparse_model`: Character; specifies the model to be used for the sparse kernel when using the gp2Scale likelihood. Defaults to `"none"`. - `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. ## Returns A `nimbleCode` object. ## Examples ```r # 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 ) ```

nsgpModel function