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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?

Alexander Shchur
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  • This question http://stats.stackexchange.com/questions/59363/having-a-conjugate-prior-deep-property-or-mathematical-accident?rq=1 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. – Erik Oct 17 '16 at 09:09
  • Also previously asked here: http://stats.stackexchange.com/questions/90969/how-to-find-conjugate-prior-for-a-given-distribution .. (but which is not answered). Not sure I follow the comment there though. – Glen_b Oct 17 '16 at 10:00
  • I closed as a duplicate of the post Erik mentioned, but if you can more clearly distinguish this one, it might stand alone. – Glen_b Oct 17 '16 at 10:05

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