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

Annalisa Cerquetti

Statistics & Probability Letters, 2007, vol. 77, issue 18, 1705-1711

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.

Keywords: Exchangeable; random; partitions; Exponential; tilting; Inverse; Gaussian; density; Random; probability; measures; Tempered; stable; laws (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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