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theorem Verification.checkerboard_xi_le_of_isCI {n : ℕ} (C : ProbabilityTheory.Copula 2) (hC : C.IsCI) (m : ℕ) (hm : 0 < m) (Q : ProbabilityTheory.Copula.IntervalPartition n) : (C.cellMass (ProbabilityTheory.Copula.IntervalPartition.uniform m hm) Q).checkerboard.chatterjeeXi ≤ C.chatterjeeXi

Uniform predictor bins and arbitrary response bins preserve the xi upper bound for every conditionally increasing copula, including singular copulas.

theorem Verification.checkerboard_xi_le_of_mtp2 {n : ℕ} (C : ProbabilityTheory.Copula 2) (hC : C.HasMTP2Density) (m : ℕ) (hm : 0 < m) (Q : ProbabilityTheory.Copula.IntervalPartition n) : (C.cellMass (ProbabilityTheory.Copula.IntervalPartition.uniform m hm) Q).checkerboard.chatterjeeXi ≤ C.chatterjeeXi

Theorem 4.2: the actual checkerboard matrix extracted from an MTP2 density.