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. FCR parallels false discovery rate: FDR concerns false rejected hypotheses among discoveries, while FCR concerns noncovering intervals among selected reports.
Scope of Application¶
Use FCR with parameter family, selection rule, interval procedure, dependence assumptions, nominal level, zero-selection convention, and width criterion stated. 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. The closest near miss sets the boundary: False discovery rate is closest: it averages false rejections among discoveries, whereas FCR evaluates interval noncoverage among selected parameters. A positive case must satisfy this test: A procedure controls FCR when it bounds the expected proportion of noncovering intervals among a data-selected set under stated assumptions.
Manages Complexity¶
Different procedures control FCR under different dependence and selection structures. Simulation should check coverage, interval width, and power-like selection behavior together. The central coverage control–interval width tradeoff is this: Stronger protection can make selected intervals less informative. A second expected rate–realized errors tension matters because Long-run control does not identify which present intervals miss.
Abstract Reasoning¶
Use three linked moves: define the full parameter family; specify the data-dependent selection rule; choose a valid selection-adjusted interval procedure. As a collapse test, the case exits when intervals are not selected data-dependently or the error criterion is probability of any miss rather than expected selected proportion. A fourth check is to compute the false-coverage proportion convention. A final check is to 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. No canonical parent prime is currently asserted; broader structural comparisons remain related-prime analogies until separately adjudicated in the DAG. It is the testing analogue. It supplies the problem setting.
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