**Sankhya:
The Indian Journal of Statistics**

2006, Volume 68, Pt. 3, 461--487

**Some Developments of the Normalized Random Measures with Independent Increments**

Laura M. Sangalli, Universitàa degli Studi di Pavia, Italy

SUMMARY. In this paper, we deal with sequences of exchangeable observations, which are conditionally independent and identically distributed with a common (random) distribution $\tau$, where $\tau$ is defined by the conditioning of a normalized random measure with independent increments. By application of a multidimensional version of the Faàa di Bruno formula, we derive explicit closed form expressions for the finite dimensional distributions and the predictive distributions of the sequence. The results are illustrated through suitable examples.

*AMS (2000) subject classification. *Primary 62F15; secondary 60G57.

*Key words and phrases. *Bayesian nonparametric inference, normalized random
measure with independent increments, species sampling sequence.