Design an e-detector

Fixes, before any Phase II observation is seen, everything the detector needs: the pre-change class and its parameters, the direction of the change to detect, the detector type (Shiryaev–Roberts or CUSUM), the family of e-values and the mixture over post-change alternatives, and the target average run length (ARL) to a false alarm.

Usage

edetect_design(
  arl = 370,
  class = edetect_classes(),
  center = NULL,
  bounds = NULL,
  sigma = NULL,
  direction = c("up", "down", "both"),
  type = c("sr", "cusum"),
  evalue = c("betting", "hoeffding"),
  delta = NULL,
  weights = NULL,
  phase1 = NULL
)

Arguments

arl

Target average run length to a false alarm. The alarm threshold is arl on the e-detector scale (equivalently alpha = 1 / arl).

class

Pre-change class, see edetect_classes().

center

Pre-change mean ("bounded", "subgaussian"), success probability ("bernoulli") or rate per unit exposure ("poisson"). May be omitted when phase1 is supplied.

bounds

Known bounds c(a, b) of the observations ("bounded" only).

sigma

Declared sub-Gaussian scale ("subgaussian" only). May be omitted when phase1 is supplied, in which case the Phase I standard deviation is used and recorded as an assumption.

direction

Change to detect: an increase ("up"), a decrease ("down") or either ("both", a half-and-half mixture of the two).

type

"sr" (Shiryaev–Roberts type, a sum of e-processes started at every time) or "cusum" (CUSUM type, a maximum). Both are e-detectors and both use the threshold arl, which for the CUSUM type is valid but conservative (Shin, Ramdas and Rinaldo, 2024, Section 2.5); "sr" is the default.

evalue

E-value family for the "bounded" class: "betting" (1 + lambda (x - center), tight for bounded data) or "hoeffding" (sub-Bernoulli exponential). Ignored by the other classes, which use their natural exponential e-values.

delta

Post-change shifts the mixture covers, in the units of the observations (positive numbers; the sign follows direction). Each shift is mapped to the bet lambda that is optimal for it in the class. The default is a geometric grid spanning small to large shifts.

weights

Mixture weights over delta, normalised internally. Default uniform.

phase1

Optional Phase I (in-control) data: a numeric vector for the "bounded" and "subgaussian" classes, or a data frame with columns x (counts) and n for "bernoulli" and "poisson". Used to set center (and sigma) when they are not declared; the source is recorded in the design and in every report.

Value

An object of class edetect_design.

Details

The guarantee is distribution-free within the class: for every pre-change distribution in it, the expected time to a false alarm is at least arl (Shin, Ramdas and Rinaldo, 2024, Theorem 2.4), and the probability of a false alarm by any time t, including data-dependent monitoring horizons, is at most t / arl (Ramdas, 2026). The price is paid in detection delay, which depends on the alternatives the mixture covers.

References

Shin, J., Ramdas, A. and Rinaldo, A. (2024). E-detectors: a nonparametric framework for sequential change detection. The New England Journal of Statistics in Data Science, 2(2), 229–260. doi:10.51387/23-NEJSDS51

Ramdas, A. (2026). Universality of e-detectors for ARL control. arXiv:2608.12660.

Examples

edetect_design(arl = 370, class = "bounded", center = 0.5, bounds = c(0, 1))
#> 
#> ── e-detector design ───────────────────────────────────────────────────────────
#> Pre-change class: "bounded"; centre 0.5 (declared)
#> Bounds: [0, 1]; e-values: "betting"
#> Direction: "up"; type: "sr"; target ARL 370 (threshold 370 on the e-detector
#> scale)
#> Mixture over 7 shifts: 0.025, 0.05, 0.1, 0.175, 0.25, 0.35, 0.45
edetect_design(arl = 500, class = "bernoulli", center = 0.02, direction = "up")
#> 
#> ── e-detector design ───────────────────────────────────────────────────────────
#> Pre-change class: "bernoulli"; centre 0.02 (declared)
#> Direction: "up"; type: "sr"; target ARL 500 (threshold 500 on the e-detector
#> scale)
#> Mixture over 7 shifts: 0.049, 0.098, 0.196, 0.343, 0.49, 0.686, 0.882
edetect_design(arl = 370, class = "subgaussian", phase1 = rnorm(100), direction = "both")
#> 
#> ── e-detector design ───────────────────────────────────────────────────────────
#> Pre-change class: "subgaussian"; centre 0.0332 (phase1, n = 100)
#> Sub-Gaussian scale: 0.9445
#> Direction: "both"; type: "sr"; target ARL 370 (threshold 370 on the e-detector
#> scale)
#> Mixture over 12 shifts: 0.236, 0.472, 0.944, 1.42, 1.89, 2.83, -0.236, -0.472,
#> -0.944, -1.42, -1.89, -2.83