Sampling with while loop issue - Initialization always the same / resetting variable

There are no ways to have PyMC distributions inside scan loops in PyMC3, this will be possible in the next major release with PyMC V4.

I have a prototype notebook here, but as you can see many things are still messy and need to be cleaned up: pymc_aeppl_scan_model.ipynb · GitHub

What you are doing in your example is wrong with using test values. That loop will only be evaluated once when you create the variables and not be rerun or updated during sampling.