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  • $\begingroup$ Possibly we could try some continuous analogue of a binomial distribution? That might lead to different options, but I am sure there are some more simple/desired cases among them. $\endgroup$ Commented Dec 13, 2024 at 16:16
  • $\begingroup$ The binomial distribution has a relationship between variance and expectation like $Var[X] = (1-p) E[X]$. Are there known distributions that match that? Or otherwise we could maybe model it as a normal distribution $X \sim N(np,np(1-p))$ and for that case a Jeffreys prior should exist and might be computed. $\endgroup$ Commented Dec 13, 2024 at 16:22
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    $\begingroup$ Relevant: stats.stackexchange.com/questions/500781/…, stats.stackexchange.com/questions/275600/…, stats.stackexchange.com/questions/113851/…, stats.stackexchange.com/questions/588863/…, stats.stackexchange.com/questions/502124/… and search for more ... $\endgroup$ Commented Dec 13, 2024 at 16:33
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    $\begingroup$ Number of trials to get a known count of successes (the observed data) would be negative binomial. $\endgroup$ Commented Dec 14, 2024 at 2:08
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    $\begingroup$ Literature on bayesian feature selection might contain some recipes - since they are concerned with inherently discrete parameters, like the number of features in a model. $\endgroup$ Commented Dec 15, 2024 at 9:08