There’s no way you can reconstruct the uncertainty analysis on the basis of the article, so it’s absolutely not you! Explaining the uncertainty analysis at the level of exposition of the article would triple the length of the article, so it’s much more “you can do this and this is sort of what it looks like” than “this is how to do this”

I don’t know how familiar you are with this kind of analysis. The probabilities we’re trying to infer from the database are a multi nominal distribution. The conjugate prior to the multinomial distribution is the Dirichlet distribution. This encodes the uncertainty in the parameters. The shown distributions are the P90-P10 ranges of the marginalized distributions for each of the parameters.

If that makes any sense at all then you can get all the missing information from the wikipedia page on the multinomial distribution. If not then I do plan an article going through this at some point, but it’s a couple of months off.

If you have a particular application in mind, then please don’t hesitate to get in touch. I’m easy to find on linkedin. You’re very welcome to write to me there.

Kind regards,

Graeme