Is there any specific reason why a Beta distribution would be chosen as a prior, other than that it is conjugate for the Binomial?

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    $\begingroup$ The beta distribution is also conjugate for the other Bernoulli trial probability distributions including Bernoulli, geometric and negative binomial. See Wikipedia's article on the beta distribution en.wikipedia.org/wiki/Beta_distribution $\endgroup$ – compbiostats Apr 25 '20 at 16:41
  • $\begingroup$ conjugacy seems a rather nice property to have (AFAIK) - in that it is equivalent to a previous experiment?! $\endgroup$ – seanv507 Apr 25 '20 at 17:26
  • $\begingroup$ have you looked at: en.wikipedia.org/wiki/Beta_distribution ? $\endgroup$ – eSurfsnake Apr 25 '20 at 19:02
  • $\begingroup$ Frequently used as priors when data are binomial and inference centers of success probability $p.$ Then $0 < p < 1$ is the natural support for a prior dist'n on $p.$ and beta distributions are well suited for that. // As mentioned above use of beta prior with binomial likelihood makes it easy to find beta posterior (because of "conjugacy" = mathematical compatibility). $\endgroup$ – BruceET Apr 25 '20 at 22:44