Monotonicity Necessity and Sufficiency (MNS)

Code:

Paper: Monotonicity: Detection, Refutation, and Ramification

Visualization

Lower Bounds on the Probability of Benefit

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Impossible Area

  • \(P(y_x)\), \(P(y_{x'})\): \((0.99, 0.99)\)
  • \(0.99 \leqslant P(y'_x, y_{x'}) \leqslant 0.99\)
  • Range: \(0\)
\(P(x) = 0.5\), \(P(x') = 0.5\)
\(P(y|x) = 0.5\)
\(P(y|x') = 0.5\)
\(P(y) = 0.5\), \(P(x, y) = 0.25\), \(P(x, y') = 0.25\), \(P(x', y) = 0.25\), \(P(x', y') = 0.25\)