Boundary-Avoiding Priors

Modeling
3

My recommendation would be the PC prior on the over-dispersion parameter. It can be found here. rejoinder.pdf (236.0 KB)

R-code for the log-density:

INLA::inla.pc.dgamma function (x, lambda = 1, log = FALSE) 
{
    inv.x = 1/x
    d = sqrt(2 * (log(inv.x) - psigamma(inv.x)))
    ld = -lambda * d - log(d) + log(lambda) - 2 * log(x) + log(psigamma(inv.x, 
        deriv = 1) - x)
    return(if (log) ld else exp(ld))
}

This is the default in INLA and it’s worked quite well in applications.

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