Sequential piecewise ensemble model — fit_piecewise

Reproduces the sequential partition-point identification algorithm of the manuscript: starting from an initial data window, candidate partition points are searched by grid search (find_partition_point()); the window is then advanced by update_every observations and, at each update, the most recent (still-unsplit) segment is re-examined for a new structural change, which is confirmed only if the pooled MSE of the best split is at least threshold lower than the MSE of leaving that segment unsplit.

Usage

fit_piecewise_ensemble(
  y,
  t = NULL,
  window = 90L,
  update_every = 20L,
  min_obs = 12L,
  criterion = "mse",
  beta_fixed = 1.5,
  threshold = 0.5,
  confirm_criterion = c("mse_threshold", "aic", "permutation"),
  alpha = 0.05,
  B = 99L
)

Arguments

y: Numeric vector of cumulative counts (the full observed series).
t: Optional numeric time index (defaults to seq_along(y)).
window: Size of the initial data window used to search for the first partition point (default 90, as in the manuscript).
update_every: Number of observations by which the window advances at each sequential update (default 20).
min_obs: Minimum admissible segment length (default 12; use 15 to match Simulation Scenario 2 of the manuscript).
criterion, beta_fixed: Passed to fit_ensemble().
threshold: Relative MSE reduction required to confirm a new partition point under confirm_criterion = "mse_threshold" (default 0.5, i.e. the split must at least halve the MSE relative to the unsplit fit — this is the rule described in the manuscript).
confirm_criterion: How a candidate split is confirmed. "mse_threshold" (default) reproduces the manuscript's rule exactly. "aic" instead compares a changepoint-penalised AIC for the split against the unsplit fit — splitting doubles the number of growth-curve parameters (three models re-fit on each side) and adds one degree of freedom for the partition-point location itself, and "aic" is the more conservative choice when a flat MSE-reduction threshold over-segments noisy real series (see the package vignette for a worked comparison on both simulated and real surveillance data). "permutation" instead performs a formal hypothesis test (permutation_test_partition()): the candidate split is confirmed only if its MSE reduction is unlikely under a null, unsplit growth process, at level alpha, properly accounting for the multiple comparisons implicit in scanning the whole candidate grid. This is the criterion we recommend when statistical significance, not just a descriptive rule, is required (e.g. for direct comparison against nonparametric permutation-based detectors such as ecp::e.divisive); it is markedly more expensive computationally than the other two.
alpha: Significance level used only when confirm_criterion = "permutation".
B: Number of permutation-test null replicates, used only when confirm_criterion = "permutation"; passed to permutation_test_partition().

Value

An object of class piecewise_fit: a list with cuts (sorted confirmed partition points), segments (list of ensemble_fit objects, one per final segment, each carrying the original time range in $t_range), fitted (full fitted curve aligned with y), and history (list of grid-search diagnostics at every update step, suitable for reproducing the manuscript's MSE-profile figures).