multispace | A 2D node / javascript based multiplayer top down space game | Game Engine library

Indeed, this is a bit of a tricky problem, but that may just needs a small update in zfit.

What you are doing is correct: simply use only the data in the desired region. However, this is not the whole story because there is a "normalization range": probabilistically speaking, it's like a conditioning on a certain region as we know the data can only be in a specific region. Hence the normalization of the PDF should only integrate over the included (LOW and HIGH) regions.

This can normally be done in two ways:

using the multispace property as you do. This should work (it is though most probably not the way to go in the future), except for a quirk in the polynomial function: the polynomials are defined from -1 to 1. Currently, the data is simply rescaled therefore to be within -1 and 1 (and for that it should use the "space" property of the PDF). This, currently, requires to be a simple space (which could also be allowed in principle, using the minimum and maximum of the limits).

As mentioned in the comments by @jtlz2, you can do a simultaneous fit. That is nothing to worry about, it is simply splitting the likelihood into two parts. As it is a product of probabilities, we can just conceptually split it into two products and multiply (or add their log).

So you can have the pdf fit the lower region and the upper at the same time. However, this does not solve the problem of the normalization: what should the PDF be normalized to? We will run into the same problem.

Space and the normalization range are however not the same. By default, the space (usually called 'obs') is also used as the default normalization range but not required. So you could use one space going from the lowest to the largest point as the obs and then set the norm range with your multispace (set_norm should do it or set_norm_range if you're using not the newest version). This, I think, should do the trick.

The actual problem is that it complains about the re-scaling to -1 and 1 that can't be done. Every polynomial which does that can also be told not to do that by using the apply_scaling=False argument. With that, you're responsible to scale the data within -1 and 1 (as the polynomials are not defined outside) and there should not be any error.