Hi Hugo, I am sorry I am a little overwhelmed by the amount of details here and I am not sure I can be very helpful right now. A general point I have is that perhaps you shouldn’t be too worried about the prior if it doesn’t influence the posterior too much, which you can try out by setting priors of different scale and comparing the posterior inference. Setting priors in general, and specifically for categorical/multinomial is a non-trivial topic and I am not sure if I can give you any good advice out of the box.