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Clarify interpretation of noise distributions #656
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dilpath
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Thanks!
doc/v2/documentation_data_format.rst
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| :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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Actually, for normal distributions it is the standard distribution (no log), while for Laplace it is the scale. I have made this clearer.
Co-authored-by: Dilan Pathirana <[email protected]>
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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
When implementing support for
LogLaplacein 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 $\log(m) \sim \mathcal{N}(\log(y), \sigma)$ , which implies $m \sim \mathcal{LN}(\log(y), \sigma)$ . For this
LogNormaldistribution in PEtab we haveLogNormal, the median isy(expof first argument). A similar interpretation holds forLogLaplace. Overall, this PR aims to clarify this.