False coverage rate¶
The expected proportion of selected confidence intervals that fail to contain their corresponding true parameters, controlled to address selective reporting in multiple-parameter inference.
Core Idea¶
The false coverage rate (FCR) is the expected proportion of reported, data-selected confidence intervals that fail to contain their corresponding true parameters. It was developed for settings where researchers inspect many results and construct or highlight intervals only for selected parameters, invalidating ordinary marginal coverage interpretations.
FCR parallels false discovery rate: FDR concerns false rejected hypotheses among discoveries, while FCR concerns noncovering intervals among selected reports. Procedures such as selection-adjusted Bonferroni or Benjamini–Yekutieli constructions seek narrow intervals while controlling the rate under stated assumptions. FCR is an expectation over repeated data and selection; it is neither a guarantee that every selected interval covers nor identical to simultaneous family-wide coverage.
Structural Signature¶
Sig role-phrases:
- parameter family. Supplies many targets considered jointly. Constitutive multiplicity. If altered: One prespecified interval does not create selection error.
- data-dependent selection. Chooses which parameters receive reported intervals. Identity-bearing mechanism. If altered: Selection changes conditional coverage behavior.
- selected confidence intervals. Estimate the chosen parameters under an adjusted procedure. Constitutive objects. If altered: Unadjusted marginal intervals may undercover after selection.
- noncoverage indicators. Record whether each selected interval misses its true parameter. Constitutive error event. If altered: Truth is theoretical or assessed in repeated sampling.
- expected false proportion. Averages false coverage divided by selected count with a declared zero-selection convention. Constitutive criterion. If altered: FCR control is not simultaneous all-interval coverage in every realized dataset.
What It Is Not¶
- FDR. Are false rejections or interval misses counted?
- Family-wise coverage. Is any miss rather than average selected proportion controlled?
- Marginal confidence interval. Was the target selected after inspection?
- Interval width. Is efficiency being mistaken for error control?
Scope of Application¶
Use FCR with parameter family, selection rule, interval procedure, dependence assumptions, nominal level, zero-selection convention, and width criterion stated.
- Genomics. Reports intervals after screening.
- Selective inference. Adjusts post-selection uncertainty.
- Multiple comparisons. Controls families of claims.
- A/B testing. Quantifies chosen effects.
- High-dimensional science. Handles thousands of parameters.
Clarity¶
Selection and interval construction are coupled; applying ordinary intervals after looking at significance can inflate noncoverage among the reported subset.
Manages Complexity¶
Different procedures control FCR under different dependence and selection structures. Simulation should check coverage, interval width, and power-like selection behavior together.
Abstract Reasoning¶
- Define the full parameter family.
- Specify the data-dependent selection rule.
- Choose a valid selection-adjusted interval procedure.
- Compute the false-coverage proportion convention.
- Verify rate and width under realistic dependence.
Knowledge Transfer¶
Post-selection error control transfers across reporting systems, but confidence-interval coverage and selected parameters delimit FCR. The nearest stopping boundary is explicit: False discovery rate is closest: it averages false rejections among discoveries, whereas FCR evaluates interval noncoverage among selected parameters. The inclusion test remains: A procedure controls FCR when it bounds the expected proportion of noncovering intervals among a data-selected set under stated assumptions. The structure no longer applies when the case exits when intervals are not selected data-dependently or the error criterion is probability of any miss rather than expected selected proportion.
Examples¶
Canonical¶
A microarray study selects genes by a multiple-testing rule and constructs adjusted confidence intervals only for those genes, using a procedure proved to bound expected noncoverage proportion.
Mapped back: parameter family → gene effects; data-dependent selection → screening rule; selected confidence intervals → adjusted intervals; noncoverage indicators → missed true effects; expected false proportion → controlled expectation.
Applied / In Practice¶
A study builds one prespecified 95% interval before seeing data. Marginal coverage is relevant, but selected-interval FCR is not the distinctive problem.
Mapped back: parameter family → one target; data-dependent selection → absent; selected confidence intervals → prespecified; noncoverage indicators → ordinary miss; expected false proportion → reduces to marginal setting.
Structural Tensions¶
T1: coverage control vs. interval width. Stronger protection can make selected intervals less informative. Diagnostic: Which procedure best balances the two?
T2: expected rate vs. realized errors. Long-run control does not identify which present intervals miss. Diagnostic: How is uncertainty communicated?
Structural–Framed Character¶
Description turns on parameter family, data-dependent selection, selected confidence intervals, noncoverage indicators, expected false proportion. Skeletal core. Error is measured among outputs selected by the same evidence that informed them. Domain-bound accent. Parameters, confidence intervals, selection, coverage, multiplicity, Bonferroni, and FDR define FCR. Transfer remains bounded because Why not prime. Selected-output error is portable; this is an inferential rate. The negative boundary is concrete: Any confidence level, family-wise error, false discovery rate, simultaneous band, selective p-value, coverage probability, Bonferroni interval, or average interval width is not automatically an FCR guarantee. FCR is statistical-evaluative: selection-dependent noncoverage is summarized and controlled as an expected proportion. Its character: confidence intervals protected against the bias of choosing what to report.
Structural Core vs. Domain Accent¶
Skeletal core. Error is measured among outputs selected by the same evidence that informed them.
Domain-bound accent. Parameters, confidence intervals, selection, coverage, multiplicity, Bonferroni, and FDR define FCR.
Why not prime. Selected-output error is portable; this is an inferential rate.
Instantiates / Related Primes¶
- False discovery rate. It is the testing analogue.
- Selective inference. It supplies the problem setting.
- No strict parent is asserted.
Neighborhood in Abstraction Space¶
False coverage rate sits in a moderately populated region (45th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Empirical Measurement & Statistical Inference Methods (50 abstractions)
Nearest neighbors
- Bootstrapping populations — 0.88
- M-Estimator — 0.88
- MAP estimator — 0.87
- Constant false alarm rate — 0.86
- Bayesian Programming — 0.86
Computed from structural-signature embeddings · 2026-10-08
Not to Be Confused With¶
- FDR. Tell: Are false rejections or interval misses counted?
- Family-wise coverage. Tell: Is any miss rather than average selected proportion controlled?
- Marginal confidence interval. Tell: Was the target selected after inspection?
- Interval width. Tell: Is efficiency being mistaken for error control?
References¶
- Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/False_coverage_rate (revision 1294430439).
- Preserved source candidate: http://www.math.tau.ac.il/~ybenja/MyPapers/benjamini_yekutieli_JASA2005.pdf
- Preserved source candidate: http://primage.tau.ac.il/libraries/theses/exeng/free/2979859.pdf
- Preserved source candidate: http://astro.temple.edu/~zhaozhg/FCR_JRSS.pdf
The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.