Clarify interpretation of noise distributions #656
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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.