Does anyone have advice/references on choosing a minimally informative prior for the shape parameter of an Erlang distribution (gamma distribution with shape parameter restricted to integer space), or a joint prior on both parameters.
My gut tells me that a discrete uniform could be a bad idea. A truncated poisson would work but will be quite informative....
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$\begingroup$ I have never seen an Erlang-k application where k is not fixed. It will be hard to find references for what you are doing. Are you running a hierarchical model? $\endgroup$– joint_pCommented Jul 11, 2013 at 21:09
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$\begingroup$ @joint_p nope not a hierarchical model. $\endgroup$– scottyazCommented Jul 11, 2013 at 21:27
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$\begingroup$ Why don't you just run with different k-s and then do bayes factor? Or use a Dirichlet prior. I am not sure if there is any benefit to modeling the order of that integer. If you think that it's necessary, how about an ordered probit link? Just use a normal as prior, add cut-points and also put a prior on those. $\endgroup$– joint_pCommented Jul 11, 2013 at 22:15
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