For a negative biomial model, where $Y_i \sim \text{NegBin}(\mu_i, \kappa)$ $$\mu_i:=\log EY_i = \mathbf{x_i} \mathbf{\beta} + \log t_i,$$ is the form of Jeffreys's prior known/published in some way that one could easily implement it e.g. in Stan?

  • $\begingroup$ does this answer your question? stats.stackexchange.com/questions/58099/… obviously it doesn't cover the stan part but that by itself would probably be off topic $\endgroup$ – jld Jan 30 '18 at 19:21
  • $\begingroup$ Are you assuming $\kappa$ is known? $\endgroup$ – jbowman Jan 30 '18 at 19:27
  • $\begingroup$ @jbownan unknown $\kappa$, unknown betas. $\endgroup$ – Björn Jan 30 '18 at 19:32
  • $\begingroup$ @Chaconne That’s for the formulation in terms of “how many tries until m successes” - not the mean rate per time unit + dispersion version. I suppose maybe re-parameterizing should give the answer for the case with just an intercept? But what about the regression setting? $\endgroup$ – Björn Jan 30 '18 at 19:35

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