# Returns posterior predictive sample from spLM object The function `spLMPredictJoint` collects posterior predictive samples for a set of new locations given a `spLM` object from the `spBayes` package. ```r spLMPredictJoint(sp.obj, pred.coords, pred.covars, start = 1, end = nrow(sp.obj$p.theta.samples), thin = 1, verbose = TRUE, n.report = 100, noisy = FALSE, method = "eigen") ``` ## Arguments - `sp.obj`: An `spLM` object returned by the `spLM` function in the `spBayes` package. - `pred.coords`: An $np x 2$ matrix of $np$ prediction location coordinates in $R^2$ (e.g., easting and northing). The first column is assumed to be easting coordinates and the second column northing coordinates. - `pred.covars`: An $np x k$ matrix of covariates matrix associated with the new locations. - `start`: Specifies the first sample included in the composition sampling. - `end`: Specifies the last sample included in the composition. The default is to use all posterior samples in `sp.obj`. - `thin`: A sample thinning factor. The default of 1 considers all samples between `start` and `end`. For example, if `thin = 10` then 1 in 10 samples are considered between `start` and `end`. - `verbose`: If `TRUE`, model specification and progress of the sampler is printed to the screen. Otherwise, nothing is printed to the screen. - `n.report`: The interval to report sampling progress. - `noisy`: If `TRUE`, then the posterior sample for the response is for the signal + error noise. The default, `FALSE`, assumes the user wants the error-free process. - `method`: Method used to decompose covariance matrix. Options are "chol", "eigen", and "svd" for the Cholesky, Eigen, and singular value decomposition approaches, respectively. ## Returns The function returns a $np \times B$ matrix of posterior predictive samples, where `B` is the number of posterior samples. The class is `jointPredicitveSample`. ## Details This function samples from the joint posterior predictive distribution of a Bayesian spatial linear model. Specifically, it is intended to be similar to the `spPredict` function in the `spBayes` except that it samples from the joint distribution instead of the marginal distribution. However, it will only work for `spLM` objects and should have the same limitations as the `spLM` and `spPredict` functions. Note that the `spRecover` function is called internally to recover the posterior samples form the posterior distribution of the spatial model. ## Author(s) Joshua French ## See Also spLM, spPredict, spRecover ## Examples ```r # Set parameters n <- 100 np <- 12 n.samples <- 10 burnin.start <- .5 * n.samples + 1 sigmasq <- 1 tausq <- 0.0 phi <- 1 cov.model <- "exponential" n.report <- 5 # Generate coordinates coords <- matrix(runif(2 * n), ncol = 2); pcoords <- as.matrix(expand.grid(seq(0, 1, len = 12), seq(0, 1, len = 12))) # Construct design matrices X <- as.matrix(cbind(1, coords)) Xp <- cbind(1, pcoords) # Specify priors starting <- list("phi" = phi, "sigma.sq"= sigmasq, "tau.sq" = tausq) tuning <- list("phi"=0.1, "sigma.sq"=0.1, "tau.sq"=0.1) priors.1 <- list("beta.Norm"=list(c(1, 2, 1), diag(100, 3)), "phi.Unif"=c(0.00001, 10), "sigma.sq.IG"=c(1, 1)) # Generate data B <- rnorm(3, c(1, 2, 1), sd = 10) phi <- runif(1, 0, 10) sigmasq <- 1/rgamma(1, 1, 1) V <- simple.cov.sp(D = dist1(coords), cov.model, c(sigmasq, 1/phi), error.var = tausq, smoothness = nu, finescale.var = 0) y <- X %*% B + rmvnorm(1, rep(0, n), V) + rnorm(n, 0, sqrt(tausq)) # Create spLM object library(spBayes) m1 <- spBayes::spLM(y ~ X - 1, coords = coords, starting = starting, tuning = tuning, priors = priors.1, cov.model = cov.model, n.samples = n.samples, verbose = FALSE, n.report = n.report) # Sample from joint posterior predictive distribution y1 <- spLMPredictJoint(m1, pred.coords = pcoords, pred.covars = Xp, start = burnin.start, verbose = FALSE, method = "chol") ```

spLMPredictJoint function