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Does the Student T distribution have a conjugate prior distribution? If so, what is it and what are the parameters?

MikeRand
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    No, the Student's $t$ distribution is not an exponential family and therefore cannot have a conjugate prior. – Xi'an Mar 05 '19 at 20:14

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Please see page 19 in this link: https://people.eecs.berkeley.edu/~jordan/courses/260-spring10/other-readings/chapter9.pdf

In general it says the Student's t distribution is not an exponential family and therefore cannot have a conjugate prior. The fact that the Student's $t$ distribution cannot enjoy a conjugate family (other than the trivial collection of all probability distributions) over the parameter space is connected with the Darmois-Pitman-Koopman lemma.

Xi'an
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nan hu
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    Re "the Student's t distribution is not an exponential family and therefore cannot have a conjugate prior": https://stats.stackexchange.com/questions/192554/aside-from-the-exponential-family-where-else-can-conjugate-priors-come-from/192675#192675 – Christoph Hanck Mar 06 '19 at 07:35