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

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    $\begingroup$ No, the Student's $t$ distribution is not an exponential family and therefore cannot have a conjugate prior. $\endgroup$
    – Xi'an
    Commented Mar 5, 2019 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.

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    $\begingroup$ Re "the Student's t distribution is not an exponential family and therefore cannot have a conjugate prior": stats.stackexchange.com/questions/192554/… $\endgroup$ Commented Mar 6, 2019 at 7:35
  • $\begingroup$ Are there any citable papers stating that the mean to a $t$-distribution does not have a conjugate prior? $\endgroup$ Commented Feb 13 at 6:07
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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

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    $\begingroup$ Please, consider expanding your answer. As it is, this seems more like a comment than an answer. $\endgroup$
    – utobi
    Commented Sep 9, 2022 at 14:37
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    $\begingroup$ 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. $\endgroup$
    – Community Bot
    Commented Sep 9, 2022 at 14:37

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