Working definition
Change-point methods search an ordered series for times where a statistical property changes. Offline methods segment a completed record; online methods monitor sequentially. Penalties, priors, minimum segment lengths, and detection delays determine what counts as a change.
Notation
τ = argmin segmented loss + penaltyH₀: θ₁ = θ₂; H₁: θ₁ ≠ θ₂Assumptions
- The changing property is defined.
- Noise and dependence are modeled.
- Detection thresholds are selected without outcome cherry-picking.
Invariants
- A detected point is conditional on model and threshold.
- Online detection occurs after evidence accumulates.
- Multiple candidate points consume an error budget.
Reproducible procedure
- Specify change type and minimum duration.
- Fit null and segmented alternatives.
- Validate with sensitivity, false-alarm simulation, and external evidence.
Error and boundary controls
- Gradual drift can resemble multiple abrupt changes.
- Outliers can trigger false points.
- Small samples make location uncertainty wide.
What this does not establish
A change near a transit or ingress does not establish correspondence beyond chance; event windows and controls must be pre-registered.
Explicit applications
2 cross-domain bridges
Tool and lot regime shifts
Detect candidate shifts in defect rate, critical dimension, or equipment telemetry.
Inputs
- ordered fab measurements
- lot boundaries
- maintenance events
Outputs
- candidate shift times
- location uncertainty
- external-evidence checklist
Transformation: Compare stable and segmented process models under a preselected false-alarm policy.
Limit: A detected shift localizes a change but does not identify the responsible chamber, material, or recipe.
Open connected system →Outcome regime-change audit
Detect business or measurement shifts independently before testing whether registered celestial windows add information.
Inputs
- objective outcome series
- operational covariates
- detection protocol
Outputs
- change windows
- location uncertainty
- non-celestial explanations
Transformation: Identify candidate changes under a controlled false-alarm process.
Limit: Temporal coincidence with a planetary event is not sufficient evidence of correspondence.
Open connected system →Authoritative references
- [1]NIST/SEMATECH e-Handbook of Statistical Methods · National Institute of Standards and Technology
Establishes: Methods for uncertainty analysis, calibration, time-series modeling, process monitoring, experimental design, reliability, and statistical comparison.
Boundary: Statistical procedures quantify evidence under a design and model; they do not repair biased sampling, outcome leakage, post-hoc hypotheses, or unmeasured confounding.