Posterior analysis for some classes of nonparametric models

Recently, James [L.F. James, Bayesian Poisson process partition calculus with an application to Bayesian Levy moving averages, Ann. Statist. 33 (2005), pp. 1771-1799.] and [L.F. James, Poisson calculus for spatial neutral to the right processes, Ann. Statist. 34 (2006), pp. 416-440.] has derived important results for various models in Bayesian nonparametric inference. In particular, in ref. [L.F. James, Poisson calculus for spatial neutral to the right processes, Ann. Statist. 34 (2006), pp. 416-440.] a spatial version of neutral to the right processes is defined and their posterior distribution derived. Moreover, in ref. [L.F. James, Bayesian Poisson process partition calculus with an application to Bayesian Levy moving averages, Ann. Statist. 33 (2005), pp. 1771-1799.] the posterior distribution for an intensity or hazard rate modelled as a mixture under a general multiplicative intensity model is obtained. His proofs rely on the so-called Bayesian Poisson partition calculus. Here we provide alternative proofs based on a different technique.