Abstract
Normalised generalised gamma processes are random probability measures that induce nonparametric prior distributions widely used in Bayesian statistics, particularly for mixture modelling. We construct a class of dependent normalised generalised gamma priors induced by a stationary population model of Moran type, which exploits a generalised Pólya urn scheme associated with the prior. We study the asymptotic scaling for the dynamics of the number of clusters in the sample, which in turn provides a dynamic measure of diversity in the underlying population. The limit is formalised to be a positive non-stationary diffusion process which falls outside well-known families, with unbounded drift and an entrance boundary at the origin. We also introduce a new class of stationary positive diffusions, whose invariant measures are explicit and have power law tails, which approximate weakly the scaling limit.
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Acknowledgments
The authors are grateful to two anonymous referees for helpful comments and to Pierpaolo De Blasi and Bertrand Lods for useful suggestions. This work was conducted while the second author was affiliated to the University of Torino and Collegio Carlo Alberto, Italy.
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The first author is supported by the European Research Council (ERC) through StG “N-BNP” 306406.
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Ruggiero, M., Sordello, M. Clustering dynamics in a class of normalised generalised gamma dependent priors. Ann Inst Stat Math 70, 83–98 (2018). https://doi.org/10.1007/s10463-016-0583-8
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DOI: https://doi.org/10.1007/s10463-016-0583-8