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.
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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.