uniform vs. logUniform prior

[JanHasenauer]

so far we only allow for uniform, however, we should in my opinion distinguish between uniform and logUniform. in most cases we use actually log-uniform as we consider a uniform distribution on log scale.

[FFroehlich]

Shouldn’t this already be addressed by parameter scale?

[yannikschaelte]

Agreed, parameterScaleUniform should do that, as described in the docs.

[JanHasenauer]

I would prefer to separate this as for normal and log normal. The prior should always be defined in the scale of the original parameter. parameterScale should only say what's used for optimization, sampling, etc.

[JanHasenauer]

I did not see parameterScaleUniform. let me check

[JanHasenauer]

If we always stick to definition on the original scale, we can in my understanding get rid of parameterScaleUniform, parameterScaleNormal and parameterScaleLaplace.

Furthermore, it appears as if it would make things easier to understand. at least for me.

[JanHasenauer]

What would currently happen if i would set prior logNormal and parameterScaleNormal?

[yannikschaelte]

here is the original discussion: #17. here is what is explicitly used: https://github.com/PEtab-dev/PEtab/blob/master/petab/sampling.py#L53

so the agreement was to always specify on linear scale, except the "parameterScale" ones allow to define directly on scale, e.g. loc-scale.

the difference is that "normal" gives a normal densitiy on the linear parameters, and the resulting values are then scaled, "logNormal" gives an exponentiated normal distribution on the linear parameters. "parameterScaleNormal" always returns a normal distribution, and does not scale (in contrast to the other 2) the samples afterwards.

[yannikschaelte]

So ... from my perspective they would mean slightly different things, in particular what we consider the base space for sampling. Anyone any opinions here? @paulstapor @jvanhoefer you implemented this in the first place?

[JanHasenauer]

to be honest, i can't follow the argument and the concept how the two scales information should be used. for me it would for instance be still unclear what happens if I set prior logNormal and parameterScaleNormal.

I would be in favour of keeping it simple and have the prior always defined for the untransformed parameter. In this case we would simple have a list of prior and corresponding parameters, but nothing else. This would in my opinion also be consistent with the current handling of bounds and nominal values, which always have to be defined for the untransformed parameter.

If we handele it like this, the parameter scale is essentially a setting for the inference algorithm but not for the problem specification. This separation is in my opinion useful.

[paulstapor]

The idea was that "parameterScale_Uniform/Normal/Laplace" should consider the parameter scale which was used.
This was not really crucial for parameterScaleNormal or parameterScaleLaplace. But I considered it important for paramterScaleUniform.

Here's the background:
We used to sample starting points uniformly in log10, our parameter scale. And in the wide majority of cases (I think), we will want to sample uniform in the scale of the parameters (as e.g. PESTO did).
However, due to our convention of denoting everything now in linear scale, we needed an option in PEtab, which encoded this type of initial point sampling. This is what "parameterScaleUniform" does. I considered "parameterScaleUniform" to be the best naming for this... But, if there are better ideas, we can change taht.

[paulstapor]

So ... from my perspective they would mean slightly different things, in particular what we consider the base space for sampling. Anyone any opinions here? @paulstapor @jvanhoefer you implemented this in the first place?

Yes, I implemented that after a Skype with @jvanhoefer.
In some cases, it might be interesting to quickly change the parameterScale and see, how this influences optimization. And parameterScaleXYZ is the exact equivalent to sampling by XYZ in Pesto back then...
As said: We may also use linearXYZ, logXYZ, log10XYZ, and logicleXYZ ...

[jvanhoefer]

I am not so familiar with the technical aspects in Pesto, so I do not see the technical implications...

I am fine with the current solution, but I would also be fine with what @JanHasenauer proposed.

[JanHasenauer]

I see that it is important to have the possibility to specify the sampling of starting points for optimisation independent of the prior. however, this should than not be in the section on priors.

I though that we agreed in the past to also allow the specification of a sampling distribution. This would keep the two things separate. By default the prior distribution should also be used for the sampling.

In the special case of uniform and log-uniform: I would simply allow to not specific a prior. In this case it would implicitly be (an unscaled) uniform or log-uniform distribution depending on the parameter transformation.