What is the [conjugate prior][1] distribution of the Dirichlet distribution?

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Edit: Since I asked this question many years ago, I've written a [Python library][2] for working with exponential families.  [Maximum likelihood estimation of the Dirichlet distribution][3] can be done using its expectation paramtrization (which is intimately related to the conjugate prior).


  [1]: http://en.wikipedia.org/wiki/Conjugate_prior
  [2]: https://github.com/NeilGirdhar/efax
  [3]: https://github.com/NeilGirdhar/efax/blob/main/examples/maximum_likelihood_estimation.py