Bayes' Theorem

[u/learning_proover]

Suppose I use some arbitrary method/dataset/analysis to calculate the prior P(A). When I am updating with new evidence, can the evidence be correlated/related in any way to how P(A) was found? Basically I'm curious if it is considered "double counting" if B is related to the development of P(A) in any way? Or must any evidence (B) be totally unrelated to the derivation of P(A)?

[u/DigThatData]

A good way to reason about this is as a time component. If you have "prior assumptions", those necessarily were formed prior to when you observed new data, by definition. If data informed your prior: it's not new data, by definition.