Boundary Behavior F1 CI Method

A Boundary Behavior F1 CI Method is a boundary-aware confidence interval method that properly handles F1 scores near 0 or 1 where symmetric intervals fail catastrophically and asymmetric methods are required.

• AKA: Extreme F1 CI Method, Boundary-Respecting F1 Interval Method, Edge Case F1 CI Method, Asymmetric Boundary F1 Method.
• Context:
  • It can typically detect when F1 approaches boundaries requiring special handling.
  • It can typically use asymmetric intervals (Wilson, BCa) that respect [0,1] constraints.
  • It can typically avoid degenerate intervals [0,0] or [1,1] that miss true parameter.
  • It can often show Wald coverage drops to ~0% while Wilson maintains >90% at boundaries.
  • It can often apply stronger variance inflation near boundaries than in center.
  • It can often be critical for medical/safety applications where F1 often near 1.
  • It can range from being a Lower Boundary Behavior F1 CI Method to being an Upper Boundary Behavior F1 CI Method, depending on its boundary focus.
  • It can range from being a Symmetric-to-Asymmetric Boundary Behavior F1 CI Method to being a Always-Asymmetric Boundary Behavior F1 CI Method, depending on its adaptation strategy.
  • It can range from being a Conservative Boundary Behavior F1 CI Method to being a Exact Boundary Behavior F1 CI Method, depending on its coverage guarantee.
  • It can range from being a Smooth Boundary Behavior F1 CI Method to being a Discrete Boundary Behavior F1 CI Method, depending on its transition type.
  • ...
• Example(s):
  • Near-Zero F1 Behaviors, such as:
    • Sample F1=0: Wald gives [0,0], Wilson gives [0, 0.12], BCa gives [0, 0.15].
    • Sample F1=0.05: Wald [-0.03, 0.13] (invalid), Wilson [0.01, 0.18] (valid).
    • Coverage: Wald ~5%, Wilson ~93%, BCa ~94% for true F1=0.05.
  • Near-One F1 Behaviors, such as:
    • Sample F1=1: Wald gives [1,1], Wilson gives [0.88, 1], BCa gives [0.85, 1].
    • Sample F1=0.98: Wald [0.94, 1.02] (invalid), Wilson [0.91, 0.995] (valid).
    • Coverage: Wald ~45%, Wilson ~95%, BCa ~94% for true F1=0.95.
  • Skewness Handlings, such as:
    • F1=0.9: Distribution strongly left-skewed, can't increase much.
    • Asymmetric CI: [0.84, 0.94] not centered on 0.9.
    • BCa acceleration parameter captures skewness automatically.
  • ...
• Counter-Example(s):
  • Center-Only F1 Method, which works for F1 ∈ [0.3, 0.7] only.
  • Symmetric F1 CI Method, which fails at boundaries.
  • Truncation Method, which clips invalid intervals post-hoc.
• See: Boundary-Aware Method, Asymmetric Confidence Interval, Wilson Score F1 Confidence Interval Method, BCa Bootstrap F1 Confidence Interval Method, Coverage Probability, Skewed Distribution, Degenerate Interval, Medical Diagnostic Application, Safety-Critical System, Wald F1 Confidence Interval Method, Boundary Constraint.

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