# Practical numerical example illustrating how bayesian p-values should be used for model checking?

Can you give a practical numerical example illustrating how bayesian p-values should be used for model checking?

• Please avoid asking multiple questions at once. You seem to be asking someone to write a full tutorial on using Bayesian p-values, rather then asking a specific question. – Tim Jun 8 at 19:27
• @Tim I already asked the other question on this: stats.stackexchange.com/questions/471085/… maybe Demetri can just move his answer to that one? Although this answer is not really answering anything, as I said, he is just saying "it depends". – user272422 Jun 8 at 19:40
• Just to further clarify that Demetri's answer was not answering the original question: the original question asked "How do I judge"; Demetri answered with "it depends." Clearly, "it depends" does not explain "how." – user272422 Jun 8 at 19:53

And this answer is no different. The posterior probability that you observe data at least as extreme as some value is not a hard and fast rule as it is in Frequentism. In my own experience, I don't use this quantity in isolation. I instead loop in subject matter experts and ask them targeted questions. For example, I might ask "how many patients out of 100 might have a max concentration: larger than $$C$$? The subject matter expert will give me some approximation which I can then use to check my models. But the important part here is that I could not know that number a priori, and so there is no "small enough" for every situation.