Online segmentation of an epidemic curve with e-detectors

Sequentially monitors daily counts against a forecast band of a growth-curve ensemble fitted to the current segment, and opens a new segment when an anytime-valid e-detector (package edetect) raises an alarm. Within a segment the ensemble is refitted every refit_every days on data observed before the day being monitored, so each band is predictable with respect to the past.

Usage

edetect_segment(
  x,
  d_min = 20L,
  arl = 1000,
  refit_every = 7L,
  chart = c("poisson", "subgaussian"),
  z = 2,
  w_min = 0.05,
  weights = c("akaike", "inverse_mse"),
  type = c("sr", "cusum"),
  beta = 1.5
)

Arguments

x: Daily counts.
d_min: Minimum segment length before monitoring starts.
arl: Target average run length to a false alarm.
refit_every: Refit interval (days) within a segment.
chart: "poisson" or "subgaussian".
z: Half-width multiplier of each model's band (0 monitors the point forecast).
w_min: Minimum ensemble weight for a model to enter the envelope.
weights: Ensemble weighting scheme.
type: e-detector type, "sr" or "cusum".
beta: Richards shape.

Value

A list with cuts (last day of each closed segment), alarms (alarm times), delay, band (matrix of monitored forecast, lower and upper band, NA on unmonitored days), segments and the final ensemble of every segment (fits).

Details

The band \([\ell_t, u_t]\) is the envelope, over the models carrying at least w_min ensemble weight, of their delta-method bands (predict_band()). Two one-sided detectors run in parallel, each with target average run length 2 * arl: an upward detector tests the composite null "conditional mean at most \(u_t\)" and a downward detector the null "at least \(\ell_t\)". If the conditional mean lies in the band, the probability of any false alarm by time \(t\) is at most \(t/\mathrm{arl}\) (union bound over the two detectors). With chart = "poisson" the detectors are Poisson u charts with exposure \(u_t\) (resp. \(\ell_t\)); with chart = "subgaussian" they monitor the negative-binomial Pearson residuals \((x_t-u_t)/s(u_t)\) and \((x_t-\ell_t)/s(\ell_t)\), \(s(\mu)=\sqrt{\mu(1+\mu/\hat\phi)}\), declared sub-Gaussian with unit scale (an approximation).