I have added information for the new initializationPriorType and objectivePriorType distributions, along with support for truncated distributions in the PEtab v2 specification. Additionally, a mathematical definition is provided for each prior, since some distributions, such as the gamma distribution, can be parameterized in different ways.

I would keep this as a draft until it is decided whether parameterScale should remain part of the PEtab standard. If parameterScale is retained, then I believe we should also keep the parameterScale priors where it makes sense. This is because inference is sometimes performed directly on log(p) (the logarithm of parameter p), as the geometry of the posterior landscape is often more favorable, and to avoid issues with transforming prior distributions, users sometimes place a prior on the log of the parameter directly—even though a prior on the log scale can be nonintuitive (for example, a uniform prior on the log scale is not uniform on the linear scale :).

I will also update the test-suite to test for correct prior evaluation on objectivePriorType for the linear priors (including testing truncated priors).