Good-Turing estimator

A statistical technique, developed by I.J. Good and Alan Turing at Bletchley Park during WWII cryptanalysis and independently motivated by R.A. Fisher and Corbet's 1940s ecological survey work, for estimating the total probability mass of events never yet observed in a sample — the "missing mass" — from how many distinct items in the sample occurred exactly once (singletons, or "monofacts"). Matters to this vault as a genuine cross-domain bridge: the same estimator keeps getting independently re-derived or re-applied wherever a field needs to reason about the unseen, from species-counting to cryptanalysis to, most recently, a formal bound on how often language models must hallucinate. Kalai & Vempala's 2023/STOC 2024 theorem builds its central hallucination-rate bound directly on this estimator, applied to facts rather than species or wheel-settings.

References

• claim-unseen-species-problem-has-dual-origin-ecology-and-cryptanalysis
• claim-singletons-are-the-diagnostic-of-the-unseen
• claim-chao-1984-estimator-extends-harris-1959-occupancy-bound
• claim-kalai-vempala-2023-hallucination-bound-is-a-rate-theorem-sorted-by-fact-regularity
• Captures: 10-inbox/raw/2026-07-11-hop-estimating-the-unseen.md, 10-inbox/raw/2026-11-02-this-weeks-ai-safety-capture-found-llm-errors.md