Two resampling schemes are supported. method = "poisson" implements
the parametric bootstrap of the manuscript's simulation study: bootstrap
pseudo-observations are drawn as \(y_k^{(b)} \sim
\mathrm{Poisson}(f_{ens}(t_k))\), appropriate when the data-generating
process is itself (approximately) Poisson, as in the simulated growth
curves used there. method = "residual" instead resamples the
standardised fitted residuals with replacement and adds them back onto
the fitted curve, which is appropriate for real surveillance counts: the
Poisson scheme assumes \(\mathrm{Var}(y_k)=f_{ens}(t_k)\), which is
routinely violated by over-dispersed daily death/case counts (reporting
batches, weekday effects), producing artificially narrow bands (see the
real-data application in the manuscript, where this is checked
directly). In both cases the full ensemble (all three growth models,
re-weighted) is refit to each replicate, and percentile confidence
limits are taken across the B replicates at every requested time
point.
Usage
ensemble_bootstrap_ci(
fit,
newdata = NULL,
method = c("poisson", "residual"),
B = 500L,
level = 0.95,
beta_fixed = 1.5
)Arguments
- fit
An
ensemble_fitobject.- newdata
Numeric vector of times at which to build the band (defaults to
fit$t; include out-of-window times for a forecast band).- method
"poisson"(default) or"residual".- B
Number of bootstrap replicates.
- level
Confidence level.
- beta_fixed
Passed to
fit_ensemble()for each replicate.