Confidence intervals for changepoint locations

Answers "where could this changepoint be?" for any result, and says which of five routes it used. show_ci = TRUE in autoplot() works only for the handful of engines that ship intervals of their own; this generic covers the rest, and (because the four routes mean genuinely different things) reports the provenance in a source column rather than presenting them as interchangeable.

Usage

cpt_confint(
  object,
  level = 0.95,
  method = c("auto", "native", "nsp", "bootstrap", "posterior", "conformal"),
  B = 200,
  seed = NULL,
  ...
)

Arguments

object

A ggcpt object.

level

Confidence/credible level. Defaults to 0.95. Honoured by the routes that compute an interval ("bootstrap", "posterior" and "nsp") and ignored by "native", which reports the interval the engine already computed at whatever level it was asked for. Note that method = "auto" resolves to "native" whenever the engine supplied one, so an explicit level can go unused there too: it is reported in the level column either way, and supplying a level the answer does not carry now warns rather than passing silently. To choose the level yourself, name a computing route.

method

Which route to use:

"auto"

(default) native if the engine supplied intervals, else posterior if it supplied one, else conformal where the change is one between exchangeable segments (a change in mean, variance, both, or distribution), else bootstrap.

"native"

the engine's own ci_lower/ci_upper (SMUCE/HSMUCE simultaneous confidence sets, strucchange break-date intervals, segmented breakpoint intervals, mcp posterior intervals, bfast break confidence intervals, and taylor's bootstrap confidence limits). The engines that supply them are the ones cpt_methods() marks in its ci column; nsp is marked there too but is reported under its own provenance below, because its regions are not intervals around an estimate.

"nsp"

Narrowest Significance Pursuit regions computed on the same series and matched to the changepoints. These are not intervals around an estimate (see nsp_wrapper()), but they are the strongest guarantee available, so the mapping is reported as source = "nsp_region" and a changepoint in no region gets NA.

"bootstrap"

within-segment residual resampling (the cpt_stability() scheme), re-running the detector and taking quantiles of the re-detected location. Model-agnostic and available for every engine; it measures the sampling variability of the procedure, conditional on the fitted segmentation, and it is not exact.

"conformal"

a distribution-free confidence set (CONCH, Hore and Ramdas 2026). Each changepoint is examined in its window between the neighbouring changepoints; every candidate split of the window is tested by permuting the observations within each side of it, and the candidates that survive at 1 - level form a set that contains the true location with probability at least level, whatever the distribution of the data, provided the observations within each segment are exchangeable (independent and identically distributed is the usual case) and the window holds one change. It needs no re-run of the detector, so it serves results built with as_ggcpt() and registered methods too. The set need not be contiguous: ci_lower and ci_upper are its hull and set_size counts its members, and the p-value of every candidate is attached as the "profile" attribute. The score matches what changed: a mean shift, a variance change, both, or a rank statistic for a change in distribution; summed over coordinates for a multivariate result. B sets the number of permutations per candidate.

"posterior"

a credible interval from the engine's posterior changepoint-probability profile (bcp, beast): the narrowest contiguous set of positions around the estimate holding level of the posterior changepoint mass in that changepoint's window, where the window is bounded by the neighbouring changepoints so two of them cannot claim the same mass twice.

Expect these to be wide, and read the width as a statement about the profile rather than about the location. Both supplying engines put roughly two-thirds of the window's mass at the estimate itself and spread the remaining third as a thin floor across every other position, so reaching a high level means swallowing that floor. Measured on a 200-point series with one clean change: level = 0.5 gives a width of 0 (the mode alone holds more than half), 0.8 gives 72 (bcp) and 91 (beast), and 0.95 gives 166 and 187, which is 83% and 94% of the series. The requested level is delivered in each case; what a wide interval says is that the posterior did not localise the change, not that the location is uncertain by that much. cpt_confint() warns when an interval covers more than half its window, for exactly that reason.

B

Bootstrap replicates for method = "bootstrap", and permutations per candidate split for method = "conformal". Defaults to 200.

seed

Optional seed (bootstrap and NSP are both random). The seed is scoped to this call: .Random.seed is saved and restored, so a seeded call inside a simulation loop does not pin the loop's own stream.

...

Passed to cpt_detect() on the bootstrap replicates, or to nsp_wrapper().

Value

A tibble with one row per changepoint: cp, ci_lower, ci_upper, level, source, plus cp_index/ci_lower_index/ci_upper_index on the original scale when the result carries a time index, and n_replicates for method = "bootstrap" (how many replicates actually contributed a draw for that changepoint), and set_size for method = "conformal" (how many locations the confidence set holds; an empty set has NA bounds and warns, because no single change between exchangeable segments fits that window). method = "nsp" returns NA bounds for a changepoint that falls in no region, which is a finding rather than a failure.

How well these cover

Measured over 120 replicates on a 200-point series with one changepoint at 100 and a jump of three standard deviations, at a nominal level of 0.95: "bootstrap" on pelt covered 0.992 of the time with a mean width of 2.2; strucchange's native intervals covered 1.000 at width 4.4; stepR's (smuce) covered 0.992 at width 4.6; and "posterior" on bcp covered 1.000 at width 157. Every route is conservative (none under-covers), and the width is what separates them. The two native routes and the bootstrap are the ones to quote; see the note on "posterior" above for why its interval is so much wider.

The conformal route was measured with cpt_confint_coverage() on the same design (300 replicates per cell, pelt, level 0.95). For a jump of three standard deviations it covered 0.960 at a mean width of 0.5 (the bootstrap: 0.973 at 2.0); for a jump of one standard deviation 0.970 at 18.6, where the bootstrap fell short of the level at 0.926 (width 25.8); under \(t_3\) noise with a jump of two, 0.963 at 3.5 (bootstrap 0.943 at 4.4). Its guarantee assumes exchangeable observations within each segment, and under AR(1) noise with \(\rho = 0.3\) it covered 0.920 (bootstrap 0.887): dependent noise shortens every interval here, and cpt_assumptions() checks for it.

References

Hore R, Ramdas A (2026). “Conformal changepoint localization.” arXiv preprint arXiv:2602.06267.

Examples

set.seed(2026)
x <- c(rnorm(80), rnorm(80, 4))
fit <- cpt_detect(x, method = "pelt")
cpt_confint(fit, method = "conformal", B = 50, seed = 1)
#> # A tibble: 1 × 6
#>      cp ci_lower ci_upper level source    set_size
#>   <int>    <int>    <int> <dbl> <chr>        <int>
#> 1    80       80       80  0.95 conformal        1
cpt_confint(fit, method = "bootstrap", B = 25, seed = 1)
#> # A tibble: 1 × 6
#>      cp ci_lower ci_upper level source    n_replicates
#>   <int>    <int>    <int> <dbl> <chr>            <int>
#> 1    80       80       80  0.95 bootstrap           25