Lower Bounds on the Probability of Benefit
Probability of
:
Benefit
ⓘ
Harm
ⓘ
\(P(y_x > y_{x'})\)
:
Lower bounds
ⓘ
Upper bounds
ⓘ
Impossible Area
\(P(y_x)\), \(P(y_{x'})\):
\((0.99, 0.99)\)
\(0.99 \leqslant P(y_x > y_{x'}) \leqslant 0.99\)
Range:
\(0\)
Observational data
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\(P(x) = 0.5\)
,
\(P(x') = 0.5\)
\(P(y|x) = 0.5\)
\(P(y|x') = 0.5\)
\(P(y) = 0.5\)
,
\(P(x, y) = 0.25\)
,
\(P(x, y') = 0.25\)
,
\(P(x', y) = 0.25\)
,
\(P(x', y') = 0.25\)
\(P(y_x) = 0.5\)
\(P(y_{x'}) = 0.5\)
\(0 \leqslant P(y_x > y_{x'}) \leqslant 0.5\)
, range:
\(0.5\)
impossible