# Sufficient statistic in a finite model

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

A statistic is sufficient when the conditional sample law given its value does not depend on theta wherever that condition has positive mass.

mko-finite-sufficient-statistic · definition · v0.10.0



## Mathematical statement

A statistic is a total map on the full sample carrier and its fibers form a partition. For every (theta,t) first compute P_theta(T=t). Define and calculate the exact fiber conditional law only on a positive-mass cell, then compare all valid theta laws at each t. Leave zero-mass conditions undefined, encoded as null in these outputs. Separate explicit nonsufficiency witnesses, the identity statistic and the constant-statistic boundary. No factorization theorem or estimator-quality conclusion is introduced.





## Representative formula (exact TeX)

S(T,t)=b





## Assumptions


- Complete finite parameter-indexed sampling laws are normalized separately under each theta.
- The statistic is total and all fibers are complete.





## Symbol scope


- S — sufficiency predicate
- T — finite statistic
- t — statistic value
- b — sufficiency Boolean





## Intuition, definition, and misconceptions

Qualify the total statistic and fiber partition first.

Compute every positive-mass conditional table.

Separate theta invariance, nonsufficiency and zero-mass boundaries.

Do not fabricate a law on a zero-mass condition or infer estimator quality merely from data reduction.





## Adopted derivation guide

[A sufficiency certificate from every fibre conditional law](https://ocme.evemisslab.com/en/derivations/derivation-mko-finite-sufficient-statistic-01/)The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.





## Prerequisites


- [Parametric statistical model](https://ocme.evemisslab.com/en/mko/mko-parametric-statistical-model/) — Use theta-indexed laws.
- [Statistical estimator](https://ocme.evemisslab.com/en/mko/mko-statistical-estimator/) — Use the statistic mapping.
- [Sampling distribution](https://ocme.evemisslab.com/en/mko/mko-sampling-distribution/) — Track the statistic law and fibers.
- [Conditional probability in finite models](https://ocme.evemisslab.com/en/mko/mko-conditional-probability/) — Define positive-mass conditional laws.





## Verification boundary

This finite-model certificate does not use the factorization theorem. Null denotes an undefined conditional law, not a zero distribution.

not_formalized

This does not mean the content is false; it means no replayable computational or formal evidence is registered yet.





## Next obligation

Add a factorization criterion.





## Same-source structured data

This page and the interactive view use the same object and existing language edition; this adds no proof or human review.

[Canonical MKO JSON](https://ocme.evemisslab.com/data/mko/finite-sufficient-statistic.json) · [Plain Markdown](https://ocme.evemisslab.com/en/mko/mko-finite-sufficient-statistic/index.md)