What is the problem with empirical priors?

In literature I sometimes stumple upon the remark, that choosing priors that depend on the data itself (for example Zellners g-prior) can be criticized from a theoretical point of view. Where exactly is the problem if the prior is not chosen independent from the data?

Answer

Generally, informative priors are typically viewed as your information about parameters (or hypotheses) before seeing the data. So any data-based prior is violating the likelihood principle since evidence from the sample is coming through the likelihood function and the prior.

Attribution
Source : Link , Question Author : muffin1974 , Answer Author : jaradniemi

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