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fix unclear subscript notation
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MaximilianFranz committed Jan 16, 2020
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13 changes: 6 additions & 7 deletions docs/usage.rst
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Expand Up @@ -497,17 +497,16 @@ Take for example the synthetic example studies in the `RLearner Paper`_ where ou

.. math::
y_i = b(X_i) + (W_i - 0.5) \cdot \tau(X_i) + \sigma \epsilon_i.
y_i = b(X) + (W - 0.5) \cdot \tau(X) + \sigma \epsilon(X).
That is to say, they start from a base value :math:`b(X_i)` and add or substract half the treatment effect :math:`\tau(X_i)`
That is to say, they start from a base value :math:`b(X)` and add or substract half the treatment effect :math:`\tau(X)`
depending on the treatment. This can be defined equivalently in our terminology as:

.. math::
\mu_{i0} = b(X_i) - \frac{1}{2}\cdot \tau, \\
\mu_{i1} = b(X_i) + \frac{1}{2}\cdot \tau, \\
y_{i0} = \mu_{i0} + \sigma \epsilon_i, \\
y_{i1} = \mu_{i1} + \sigma \epsilon_i.
\mu_{0} = b(X) - \frac{1}{2}\cdot \tau, \\
\mu_{1} = b(X) + \frac{1}{2}\cdot \tau, \\
y_{0} = \mu_{0} + \sigma \epsilon(X), \\
y_{1} = \mu_{1} + \sigma \epsilon(X).
We encourage users of JustCause to start their considerations with the terminology introduced at the top of this document.

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