# Posterior prediction for the NSGP `nsgpPredict` conducts posterior prediction for MCMC samples generated using nimble and nsgpModel. ```r nsgpPredict( model, samples, coords.predict, predict.process = TRUE, constants = list(), 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. ## Returns 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 ```r ## Not run: # 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 ) ## End(Not run) ```

nsgpPredict function