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refs #92 doc updats
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AnthonyLim23 committed Aug 8, 2024
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6 changes: 2 additions & 4 deletions docs/source/cf_methods.rst
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Expand Up @@ -71,13 +71,13 @@ where :math:`P(D | M)` is the probability of the data given the model, :math:`P(
The probability of the data will be the same for all models, so by taking a ratio the term can be removed

.. math::
:name: odds
:label: odds
O_{21} = \frac{P(M_2 | D)}{P(M_1 | D) = \frac{P(D | M_2)P(M_2)}{P(D | M_1)P(M_1)}
where :math:`0_{21}` is the odds factor for models two (:math:`M_2`) and one (:math:`M_1`).
Assuming that there is no prior knowledge then :math:`P(M_1) \approx P(M_2)`.
Then equation :numref:`odds` can be simplified to
Then equation :math:numref:`odds` can be simplified to

.. math::
O_{21} = \frac{P(D | M_2)}{P(D | M_1)},
Expand All @@ -93,8 +93,6 @@ To evaluate the odds factor, the probability of the data given the model needs t
This is written as

.. math::
:label: P(D|M)
P(D | M) = \int_\omega d\undeline{\theta} \quad P(D| \underline{\theta}, M)P(\underline{\theta} | M)
where the integral over :math:`\omega` is over the available parameter space for :math:`\underline{\theta}`.
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