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refs #92 BIC
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AnthonyLim23 committed Nov 19, 2024
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8 changes: 4 additions & 4 deletions docs/source/cf_methods.rst
Original file line number Diff line number Diff line change
Expand Up @@ -409,17 +409,17 @@ Lets define the difference between two neighbouring models to be

.. math::
\Delta = \ln{[P(D|M_{N+1})} - \ln{[P(D|M_N)]}.
\Delta = \ln{[P(D|M_{N+1})]} - \ln{[P(D|M_N)]}.
Hence,

.. math::
\Delta = \ln(4\pi) - \ln{([x_\mathrm{max} - x_\mathrm{min}]A_\mathrm{max})} - \ln{(\sqrt{\det{H_{N+1})} - \frac{\chi^2_{N+1}}{2} + \ln{(\sqrt{\det{H_{N})} + \frac{\chi^2_{N}}{2},
\Delta = \ln(4\pi) - \ln{([x_\mathrm{max} - x_\mathrm{min}]A_\mathrm{max})} - \ln{(\sqrt{\det{H_{N+1}}})} - \frac{\chi^2_{N+1}}{2} + \ln{(\sqrt{\det{H_{N}}})} + \frac{\chi^2_{N}}{2},
which can be rearranged to

.. math::
\Delta = \ln(4\pi) - \ln{([x_\mathrm{max} - x_\mathrm{min}]A_\mathrm{max})} - \ln{\left(\frac{\sqrt{\det{H_{N+1}}}{\sqrt{\det{H_N}}}}\right)} - \frac{1}{2}(\chi^2_{N+1} - \chi^2_{N}),
\Delta = \ln(4\pi) - \ln{([x_\mathrm{max} - x_\mathrm{min}]A_\mathrm{max})} - \ln{\left(\frac{\sqrt{\det{H_{N+1}}}}{\sqrt{\det{H_N}}}\right)} - \frac{1}{2}(\chi^2_{N+1} - \chi^2_{N}),
w

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