Question 27104: Average Coverage, Posterior Probability and Selection-Adjusted Coverage Are Different Quantities

Original question and givens

Use mode=invalid_procedure and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[4,6],[2,6]],[[2,6],[4,6]]],"intervals":[[4,3],[4,4]]}. Give (mode, procedure_valid, validation_error, procedure_qualification_claim).

• G001 — Use mode=invalid_procedure and complete model={"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[4,6],[2,6]],[[2,6],[4,6]]],"intervals":[[4,3],[4,4]]}. Give (mode, procedure_valid, validation_error, procedure_qualification_claim).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-finite-confidence-interval-coverage

Step-by-step derivation

source roles = [ci-interpretation-boundary]

derived = [[mode, procedure_valid, validation_error, procedure_qualification_claim]]

source roles = [{'theta_values': [0, 1], 'samples': ['a', 'b'], 'probability_rows': [[[4, 6], [2, 6]], [[2, 6], [4, 6]]], 'intervals': [[4, 3], [4, 4]]}]

derived = [No, interval lower endpoint exceeds upper endpoint, No]

Reverse checks

• S002 · premise_and_result_audit — Reverse-check the complete original data,step operands and premises;finite checks,conditional named-theorem use and general formal proof remain distinct.
• S001 · premise_and_result_audit — Reverse-check the complete original data,step operands and premises;finite checks,conditional named-theorem use and general formal proof remain distinct.

Result

(invalid_procedure, No, interval lower endpoint exceeds upper endpoint, No)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.