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Does there exists a certain formal procedure one has to go through before being able to claim that no conjugate prior $p(\theta)$ exists for the given likelihood function $p(X | \theta)$?

In other words, how can one be sure that a conjugate prior is truly impossible to find, rather than that one has simply failed to do so due to a lack of experience or intuition?

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  • $\begingroup$ This question stats.stackexchange.com/questions/59363/… is related to the point of being a duplicate, but it would be nice to get answer that goes a bit more into details than providing a link. $\endgroup$
    – Erik
    Commented Oct 17, 2016 at 9:09
  • $\begingroup$ Also previously asked here: stats.stackexchange.com/questions/90969/… .. (but which is not answered). Not sure I follow the comment there though. $\endgroup$
    – Glen_b
    Commented Oct 17, 2016 at 10:00
  • $\begingroup$ I closed as a duplicate of the post Erik mentioned, but if you can more clearly distinguish this one, it might stand alone. $\endgroup$
    – Glen_b
    Commented Oct 17, 2016 at 10:05

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