A dynamic Dirichlet prior with concentration θ/k is the symmetric Dirichlet specification that keeps the Gini-Simpson index non-degenerate and interpretable as richness grows, and Poisson-Dirichlet priors give posterior means that are convex combinations of the unbiased estimate and the prior mean.
By (29), this happens if (i)θgoes to zero, (ii)Kdegenerates at one or (iii)Kdegenerates at infinity withθbeing infinite
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Nonparametric Bayesian inference for the Gini-Simpson index
A dynamic Dirichlet prior with concentration θ/k is the symmetric Dirichlet specification that keeps the Gini-Simpson index non-degenerate and interpretable as richness grows, and Poisson-Dirichlet priors give posterior means that are convex combinations of the unbiased estimate and the prior mean.