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A note on Bayesian nonparametric priors derived from exponentially tilted Poisson-Kingman models

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  • Cerquetti, Annalisa

Abstract

We derive the class of normalized generalized Gamma processes from Pitman's Poisson-Kingman models [Pitman, J., 2003. Poisson-Kingman partitions. In: Goldstein, D.R., (Ed.), Science and Statistics: A Festschrift for Terry Speed, IMS Lecture Notes-Monograph Series, vol. 40. Institute of Mathematical Statistics, Hayward, CA, pp. 1-34.] with tempered [alpha]-stable mixing distribution. Relying on this construction it can be shown that in Bayesian nonparametrics, results on quantities of statistical interest under those priors, like the analogous of the Blackwell-MacQueen prediction rules or the distribution of the number of distinct elements observed in a sample, arise as immediate consequences of Pitman's results.

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  • Cerquetti, Annalisa, 2007. "A note on Bayesian nonparametric priors derived from exponentially tilted Poisson-Kingman models," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1705-1711, December.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:18:p:1705-1711
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    References listed on IDEAS

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    1. Neil Shephard & Ole E. Barndorff-Nielsen & University of Aarhus, 2001. "Normal Modified Stable Processes," Economics Series Working Papers 72, University of Oxford, Department of Economics.
    2. 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.
    3. Hansen, Ben & Pitman, Jim, 2000. "Prediction rules for exchangeable sequences related to species sampling," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 251-256, February.
    4. Lancelot F. James & Antonio Lijoi & Igor Pruenster, 2005. "Bayesian Inference via Classes of Normalized Random Measures," ICER Working Papers - Applied Mathematics Series 5-2005, ICER - International Centre for Economic Research.
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    1. Samer A. Kharroubi, 2018. "Posterior simulation via the exponentially tilted signed root log-likelihood ratio," Computational Statistics, Springer, vol. 33(1), pages 213-234, March.
    2. Argiento, Raffaele & Guglielmi, Alessandra & Pievatolo, Antonio, 2010. "Bayesian density estimation and model selection using nonparametric hierarchical mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 816-832, April.

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