Poisson univariate

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Suppose where are iid observations from the Poisson distribution with mass function:

In the parameterization above the parameter represents the mean and the variance.

Overall Recommended (OR) prior

Formal endorsements

The OR prior is the Jeffreys prior and also the reference prior.

Posterior propriety

The posterior distribution of the OR prior is


where represents the gamma distribution with mean .


  • A proper prior that has the OR prior as the limiting case is with .