Prediction of latent process at new spatial or temporal locations

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)

Arguments

mod_out: an object returned by any model fit under fixed hyperparameters or using predictive stacking, i.e., spLMexact(), spLMstack(), spGLMexact(), spGLMstack(), svcLMexact(), svcLMstack(), svcGLMexact(), svcGLMstack(), stvcGLMexact(), stvcGLMstack(), stvcLMexact() or stvcLMstack().
coords_new: new spatial coordinates (an \(n_{new} \times 2\) matrix) or, for the spatial-temporal models, a list with tags sp (an \(n_{new} \times 2\) matrix) and time (a vector or one-column matrix) at which the latent process, the mean, and the response is to be predicted.
covars_new: new covariates at the new coordinates: a matrix or, for the varying coefficients models (svc and stvc), a list with tags fixed (covariates with fixed effects) and vc (covariates with spatially or spatially-temporally varying coefficients). 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.

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.

Author

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

Examples

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

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

# fit a spatial linear model using predictive stacking
cand.mod <- candidateModels(list(phi = c(2, 4, 6), nu = c(1, 1.5, 1.75),
                                 noise_sp_ratio = c(0.1, 0.25)), "cartesian")
mod1 <- spLMstack(y_gauss ~ x1 + x2, data = dat_train,
                  coords = as.matrix(dat_train[, c("s1", "s2")]),
                  cor.fn = "matern",
                  candidate.models = cand.mod,
                  n.samples = 1000, loopd.method = "exact",
                  parallel = FALSE, verbose = TRUE)
#> 
#> STACKING WEIGHTS:
#> 
#>            | phi | nu   | noise_sp_ratio | weight |
#> +----------+-----+------+----------------+--------+
#> | Model 1  |    2|  1.00|            0.10| 0.000  |
#> | Model 2  |    4|  1.00|            0.10| 0.000  |
#> | Model 3  |    6|  1.00|            0.10| 0.000  |
#> | Model 4  |    2|  1.50|            0.10| 0.000  |
#> | Model 5  |    4|  1.50|            0.10| 0.000  |
#> | Model 6  |    6|  1.50|            0.10| 0.000  |
#> | Model 7  |    2|  1.75|            0.10| 0.000  |
#> | Model 8  |    4|  1.75|            0.10| 0.189  |
#> | Model 9  |    6|  1.75|            0.10| 0.000  |
#> | Model 10 |    2|  1.00|            0.25| 0.000  |
#> | Model 11 |    4|  1.00|            0.25| 0.000  |
#> | Model 12 |    6|  1.00|            0.25| 0.000  |
#> | Model 13 |    2|  1.50|            0.25| 0.000  |
#> | Model 14 |    4|  1.50|            0.25| 0.000  |
#> | Model 15 |    6|  1.50|            0.25| 0.000  |
#> | Model 16 |    2|  1.75|            0.25| 0.000  |
#> | Model 17 |    4|  1.75|            0.25| 0.000  |
#> | Model 18 |    6|  1.75|            0.25| 0.811  |
#> +----------+-----+------+----------------+--------+
#> 

# prepare new coordinates and covariates for prediction
sp_pred <- as.matrix(dat_pred[, c("s1", "s2")])
X_new <- cbind(1, dat_pred$x1, dat_pred$x2)

# 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)

# compare the predicted spatial effects with the truth
z_pred <- apply(post_samps$z.pred, 1, median)
cor(z_pred, dat_pred$z_true)
#> [1] 0.9977931