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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

2 Answers2

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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
  • Are there any citable papers stating that the mean to a $t$-distribution does not have a conjugate prior? – Snowy Baboon Feb 13 '24 at 06:07
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Student t-distribution does not have conjugate prior for the degrees of the freedom. However, even so, there are several priors that could be used for the degrees of the freedom.

https://www.mdpi.com/2075-1680/11/9/462

user367365
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    Please, consider expanding your answer. As it is, this seems more like a comment than an answer. – utobi Sep 09 '22 at 14:37
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    As it’s currently written, your answer is unclear. Please [edit] to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. – Community Sep 09 '22 at 14:37