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

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. (C) 2007 Elsevier B.V. All rights reserved.