I am trying to build up the model that would be able to sample countries, universities or ages of a set of people in a data set. Imagine that I could devote to each of the components, values from
0 up to the number of existing countries or universities. For instance
GB:0, US:1, Germany:2, France:3, ..., the same for different universities. What is the best distribution to be used as priors to sample such properties in my data set? Can I use the Poisson distribution for all, if I consider them as integer values?