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When implementing support for LogLaplace in PEtab.jl, I realized that the interpretation of the noise distributions in the spec is not entirely clear. In particular, for the supported distributions, the model output is not assumed to be the mean or location of the data distribution, but rather its median.

For example, let ($m$) be the measured value, $y := \text{observableFormula}$ the simulated value, and $\sigma$ the noise. For the LogNormal distribution in PEtab we have $\log(m) \sim \mathcal{N}(\log(y), \sigma)$, which implies $m \sim \mathcal{LN}(\log(y), \sigma)$. For this LogNormal, the median is y (exp of first argument). A similar interpretation holds for LogLaplace. Overall, this PR aims to clarify this.

@sebapersson sebapersson requested a review from a team as a code owner December 17, 2025 09:28
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Thanks!

:math:`y:=\text{observableFormula}` the simulated value
(the location parameter of the noise distribution),
(the median of the noise distribution),
and :math:`\sigma` the scale parameter of the noise distribution
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Same problem here, right? For the log-normal distribution, sigma wouldn't be the scale but its logarithm?

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@sebapersson sebapersson Jan 18, 2026

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Actually, for normal distributions it is the standard distribution (no log), while for Laplace it is the scale. I have made this clearer.

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Thanks, now just for consistency and to make the table narrower, I'll shorten the other descriptions too.

Removes the horizontal scrollbar on the table for me: https://petab--656.org.readthedocs.build/en/656/v2/documentation_data_format.html#noise-distributions

@sebapersson sebapersson merged commit 11f8e88 into PEtab-dev:main Jan 19, 2026
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@sebapersson sebapersson deleted the noise_distributions branch January 19, 2026 11:18
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4 participants