Generate posterior predictive samples from a MIDAS model

Generates posterior predictive samples from a fitted MIDAS model using posterior samples of the latent linear predictor. The function supports Gaussian, Poisson, and binomial response distributions.

Usage

predict_midas(model, family = "gaussian", Ntrials = NULL, nsamples = 1000)

Arguments

model: A fitted MIDAS model returned by fit_Minla_spatial().
family: Character string specifying the likelihood family. Supported values are "gaussian", "poisson", and "binomial". Defaults to "gaussian".
Ntrials: Optional vector specifying the number of trials for each observation when family = "binomial". If omitted, the function attempts to use the Ntrials column in model$data_final.
nsamples: Positive integer specifying the number of posterior samples used to generate the predictive distribution. Defaults to 1000.

Value

A list with two components:

computed_y

A list containing posterior predictive summaries:

mean: Posterior predictive mean for each observation.
sd: Posterior predictive standard deviation for each observation.
q2.5: 2.5% posterior predictive quantile for each observation.
q97.5: 97.5% posterior predictive quantile for each observation.

samples

A list containing posterior samples of the latent predictor and, for Gaussian responses, the posterior samples of the observation variance.

Details

For a Gaussian response, posterior samples of the observation variance are obtained from the posterior samples of the Gaussian precision parameter and used to generate predictive observations. For Poisson and binomial responses, observations are generated using the appropriate inverse-link function.

Examples

if (FALSE) { # \dontrun{
if (requireNamespace("INLA", quietly = TRUE)) {
  data(data_spatialpoisson_example)

  Midas_x1 <- prepare_Minla_spatial(
    x = data_spatialpoisson_example$data_x1$x1,
    loc_x = data_spatialpoisson_example$data_x1$loc,
    constraint = "hyperbolic",
    K = 0:29,
    m = 30,
    svc = FALSE
  )

  fit <- fit_Minla_spatial(
    formula = y ~ 1,
    data = data_spatialpoisson_example$data_y,
    loc_var = "loc",
    time_var = "Time",
    family = "poisson",
    hf_input = list(Midas_x1),
    inla_options = list(verbose = FALSE)
  )

  predictions <- predict_midas(
    model = fit,
    family = "poisson",
    nsamples = 1000
  )

  # Inspect posterior predictive summaries
  head(predictions$computed_y$mean)
  head(predictions$computed_y$q2.5)
  head(predictions$computed_y$q97.5)
}
} # }