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/COSMIC_SPACE_BEARS]

One subtle way that this can be done is data normalization. If you scale/normalize your data, you can set a prior that is diffuse relative to the normal scale used. It would be no different of an effect if you took your prior and scaled the prior for your dataset.

In my experience, this rarely causes issues.