diff --git a/doc/v2/documentation_data_format.rst b/doc/v2/documentation_data_format.rst index 0365154d..064b4f02 100644 --- a/doc/v2/documentation_data_format.rst +++ b/doc/v2/documentation_data_format.rst @@ -916,6 +916,20 @@ Detailed field description Prior distributions ~~~~~~~~~~~~~~~~~~~ +The prior distributions supported for the +:ref:`MAP objective function and for Bayesian inference ` +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 `__., then the following prior distributions are supported: