posteriorPredict: Prediction of latent process at new spatial or temporal locations

Description

A function to sample from the posterior predictive distribution of the latent spatial or spatial-temporal process.

Usage

posteriorPredict(mod_out, coords_new, covars_new, joint = FALSE, nBinom_new)

Value

A modified object with the class name preceeded by the identifier pp separated by a .. For example, if input is of class spLMstack, then the output of this prediction function would be pp.spLMstack. The entry with the tag samples is updated and will include samples from the posterior predictive distribution of the latent process, the mean, and the response at the new locations or times. An entry with the tag prediction is added and contains the new coordinates and covariates, and whether the joint posterior predictive samples were requested.

Arguments

mod_out: an object returned by any model fit under fixed hyperparameters or using predictive stacking, i.e., spLMexact(), spLMstack(), spGLMexact(), spGLMstack(), stvcGLMexact(), or stvcGLMstack().
coords_new: a list of new spatial or spatial-temporal coordinates at which the latent process, the mean, and the response is to be predicted.
covars_new: a list of new covariates at the new spatial or spatial-temporal coordinates. See examples for the structure of this list.
joint: a logical value indicating whether to return the joint posterior predictive samples of the latent process at the new locations or times. Defaults to FALSE.
nBinom_new: a vector of the number of trials for each new prediction location or time. Only required if the model family is "binomial". Defaults to a vector of ones, indicating one trial for each new prediction.

Author

Soumyakanti Pan span18@ucla.edu,
Sudipto Banerjee sudipto@ucla.edu

Examples

Run this code

set.seed(1234)
# training and test data sizes
n_train <- 100
n_pred <- 10

# Example 1: Spatial linear model
# load and split data into training and prediction sets
data(simGaussian)
dat <- simGaussian
dat_train <- dat[1:n_train, ]
dat_pred <- dat[n_train + 1:n_pred, ]

# fit a spatial linear model using predictive stacking
mod1 <- spLMstack(y ~ x1, data = dat_train,
                  coords = as.matrix(dat_train[, c("s1", "s2")]),
                  cor.fn = "matern",
                  params.list = list(phi = c(1.5, 3, 5), nu = c(0.75, 1.25),
                                     noise_sp_ratio = c(0.5, 1, 2)),
                  n.samples = 1000, loopd.method = "psis",
                  parallel = FALSE, solver = "ECOS", verbose = TRUE)

# prepare new coordinates and covariates for prediction
sp_pred <- as.matrix(dat_pred[, c("s1", "s2")])
X_new <- as.matrix(cbind(rep(1, n_pred), dat_pred$x1))

# carry out posterior prediction
mod.pred <- posteriorPredict(mod1, coords_new = sp_pred, covars_new = X_new,
                             joint = TRUE)

# sample from the stacked posterior and posterior predictive distribution
post_samps <- stackedSampler(mod.pred)

# analyze posterior samples
postpred_z <- post_samps$z.pred
post_z_summ <- t(apply(postpred_z, 1, function(x) quantile(x, c(0.025, 0.5, 0.975))))
z_combn <- data.frame(z = dat_pred$z_true, zL = post_z_summ[, 1],
                      zM = post_z_summ[, 2], zU = post_z_summ[, 3])
library(ggplot2)
ggplot(data = z_combn, aes(x = z)) +
  geom_errorbar(aes(ymin = zL, ymax = zU), width = 0.05, alpha = 0.15, color = "skyblue") +
  geom_point(aes(y = zM), size = 0.25, color = "darkblue", alpha = 0.5) +
  geom_abline(slope = 1, intercept = 0, color = "red", linetype = "solid") +
  xlab("True z1") + ylab("Posterior of z1") + theme_bw() +
  theme(panel.background = element_blank(), aspect.ratio = 1)