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I'd like to choose an uninformative prior for the scale and shape parameters of the Gamma distribution. Any help and suggestions will be appreciated.

kjetil b halvorsen
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desert_ranger
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    There is no completely 'flat' gamma prior among proper distributions (with densities integrating to unity). The closest you can get is to use _very_ small shape and rate parameters. (Then, for example, with a Poisson likelihood, the posterior depends very largely on the likelihood and hardly at all on the prior.) – BruceET Mar 04 '21 at 02:33
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    The use of "uninformative" or "noninformative" should be abandoned in favour of "reference" as there is no such thing (see my answer [there](https://stats.stackexchange.com/a/20535/7224)). One approach to reference priors is Jeffreys', which alas involves a digamma function for the shape parameter, unless one restricts the shape to be an integer. – Xi'an Mar 04 '21 at 08:36

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