diff --git a/README.adoc b/README.adoc index 824338d..93cbc35 100644 --- a/README.adoc +++ b/README.adoc @@ -305,3 +305,23 @@ If you use ZeroProb.jl in research, please cite: * **Author:** Jonathan D.A. Jewell * **GitHub:** https://github.com/hyperpolymath/ZeroProb.jl * **Issues:** https://github.com/hyperpolymath/ZeroProb.jl/issues + +== Applications in practice + +The worked case is permutation testing, as in MetaManifold's PERMANOVA +integration (the theorems: +link:https://github.com/hyperpolymath/MetaManifold-WebUI/blob/7d5e9a4/proofs/agda/MetaManifold/Permanova.agda[proofs/agda/MetaManifold/Permanova.agda], +pinned on the fork's `main` at 7d5e9a4 and proposed upstream as +link:https://github.com/JoshuaJewell/MetaManifold-WebUI/pull/55[PR #55], +with the Julia oracle at +link:https://github.com/hyperpolymath/MetaManifold-WebUI/blob/7d5e9a4/test/unit/test_permanova.jl[test/unit/test_permanova.jl]): +for `B` permutations the smallest attainable p-value is the +*floor* `1/(B+1)` -- attained exactly when no permutation reaches the +observed statistic -- and the proved theorems pin that floor. What ZeroProb +adds in practice is the honest language around it: a p-value at the floor is +near-zero but *not* measure-zero, and any claim of the form "essentially +impossible" must survive the same scrutiny as a density-ratio or +epsilon-neighbourhood argument. Pipelines that report "p = 0" for +insufficient permutations are publishing a measure-zero claim about a +discrete test -- this library is where that claim goes to be checked +before it reaches a figure.