Posterior cross-validation for rspde_lme models — posterior

Performs cross-validation on objects fitted with rspde_lme and computes common predictive scores. The interface mirrors MetricGraph::posterior_crossvalidation so that the two can be used interchangeably for graph-based and non-graph rSPDE fits. Pure OLS fits (rspde_lme(formula, data) with no model) are also supported: predictions reduce to evaluating the covariates at the test locations, with predictive variance $\sigma_\epsilon^2 \, (1 + x^\top (X^\top X)^{-1} x)$.

For true_CV = FALSE (default, "pseudo" cross-validation) the model parameters are kept fixed at the estimates from the full fit and only the held-out points are masked at prediction time. When use_precomputed = TRUE the parameter-dependent structures (updated rSPDE operator and the precision matrix Q) are computed once and reused across folds, mirroring the advanced_options$precompute_data / na_test_idx path of predict.rspde_lme.

For true_CV = TRUE the model is refit on each training fold (with the held-out response values set to NA). The previous fit is forwarded via previous_fit so that the optimisation starts from the full-data estimates.

Usage

posterior_crossvalidation(
  object,
  scores = c("logscore", "crps", "scrps", "mae", "rmse"),
  mode = "k-fold",
  k = 10,
  percentage = 20,
  number_folds = 10,
  train_test_indices = NULL,
  true_CV = FALSE,
  factor = 1,
  tibble = TRUE,
  parallel_folds = FALSE,
  parallel_fitting = FALSE,
  n_cores = parallel::detectCores() - 1,
  print = FALSE,
  seed = NULL,
  return_indices = FALSE,
  use_precomputed = TRUE,
  data = NULL,
  nelder_mead_init = FALSE
)

Arguments

object: A fitted object of class rspde_lme, or a (preferably named) list of such objects. When a list is supplied, the function is applied to each element and the scores are returned in a single data.frame / tibble.
scores: Character vector of scores to compute. Possible values are "logscore", "crps", "scrps", "mae" and "rmse".
mode: One of "k-fold", "loo" or "lpo".
k: Number of folds for k-fold cross-validation. Default is 10.
percentage: Percentage (1-99) of observations used for training in leave-percentage-out ("lpo") cross-validation. Default is 20.
number_folds: Number of folds for "lpo". Default is 10.
train_test_indices: Optional pre-specified list of folds. Each element must be a list with integer vectors train and test giving positions into the fitted observations (length object$nobs). When supplied, mode, k, percentage and number_folds are ignored.
true_CV: If TRUE the model is refit on every training fold; if FALSE (default) the original fitted parameters are reused (pseudo cross-validation).
factor: Multiplier applied to the mean of each score (default 1).
tibble: If TRUE (default), the returned scores are coerced to a tibble (requires the tidyr package).
parallel_folds: Process folds in parallel. Default FALSE.
parallel_fitting: Run the per-fold model refit in parallel (only relevant when true_CV = TRUE). Default FALSE. parallel_folds and parallel_fitting cannot both be TRUE.
n_cores: Number of cores for parallel computation. Default parallel::detectCores() - 1.
print: Print progress messages.
seed: Random seed for fold creation reproducibility.
return_indices: If TRUE the train/test indices used in each fold are also returned.
use_precomputed: If TRUE (default) the parameter-dependent structures used by predict.rspde_lme are precomputed once and reused across folds. Only relevant when true_CV = FALSE.
data: Optional data.frame containing the original data used to fit the model. Required for non-graph fits with non-trivial covariates (e.g. factors or transformations), where the design matrix stored in object$model_matrix is insufficient to rebuild the covariates at the test locations. Ignored for graph-based fits, where the data is taken from the metric graph.
nelder_mead_init: Logical, forwarded to rspde_lme when true_CV = TRUE. Default is FALSE: per-fold refits warm-start from the full-fit parameters via previous_fit, so the Nelder-Mead pre-pass adds little except cost. Set to TRUE to re-enable it for robustness if the full fit is itself suspected of being a poor local optimum.

Value

A list with elements

mu: vector of posterior means, one per observation
var: vector of posterior variances (including measurement error), one per observation
scores: a data.frame (or tibble) with the requested aggregated scores
indices: list of train/test indices used (if return_indices = TRUE)