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Clarify prior & bounds #655

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Clarify prior & bounds
dweindl Dec 11, 2025
63bc8ba
Update doc/v2/documentation_data_format.rst
dweindl Dec 12, 2025
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14 changes: 14 additions & 0 deletions doc/v2/documentation_data_format.rst
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Expand Up @@ -916,6 +916,20 @@ Detailed field description
Prior distributions
~~~~~~~~~~~~~~~~~~~

The prior distributions supported for the
:ref:`MAP objective function and for Bayesian inference <v2_objective_function>`
are listed below. PEtab only supports univariate prior distributions.
The probability density functions (PDFs) below assume that the parameter bounds
are wide enough to not truncate the distributions. If the parameter bounds
are narrower than the distribution's support, the distributions are truncated,
resulting in the following truncated prior distribution:

.. math::
\pi_{\text{trunc}}(x) = \frac{\pi(x)}{\text{CDF}(\text{upperBound}) - \text{CDF}(\text{lowerBound})}

where :math:`\pi(x)` is the PDF of the non-truncated distribution
and :math:`\text{CDF}(\cdot)` its cumulative distribution function.

Let :math:`x` denote the parameter value and :math:`\Gamma` the
`Gamma function <https://en.wikipedia.org/wiki/Gamma_function>`__.,
then the following prior distributions are supported:
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