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Clustering dynamics in a class of normalised generalised gamma dependent priors

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  • Matteo Ruggiero

    (University of Torino
    Collegio Carlo Alberto)

  • Matteo Sordello

    (University of Pennsylvania)

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.

Suggested Citation

  • Matteo Ruggiero & Matteo Sordello, 2018. "Clustering dynamics in a class of normalised generalised gamma dependent priors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 83-98, February.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:1:d:10.1007_s10463-016-0583-8
    DOI: 10.1007/s10463-016-0583-8
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    References listed on IDEAS

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    1. Lijoi, Antonio & Mena, Ramses H. & Prunster, Igor, 2005. "Hierarchical Mixture Modeling With Normalized Inverse-Gaussian Priors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1278-1291, December.
    2. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "Controlling the reinforcement in Bayesian non‐parametric mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 715-740, September.
    3. J. E. Griffin & M. Kolossiatis & M. F. J. Steel, 2013. "Comparing distributions by using dependent normalized random-measure mixtures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 499-529, June.
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