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

Bayesian nonparametric analysis of Kingman's coalescent

Kingman's coalescent is one of the most popular models in population genetics. It describes the genealogy of a population whose genetic composition evolves in time according to the Wright-Fisher model, or suitable approximations of it belonging to the broad class of Fleming-Viot processes. Ancestral inference under Kingman's coalescent has had much attention in the literature, both in practical data analysis, and from a theoretical and methodological point of view. Given a sample of individuals taken from the population at time $t>0$, most contributions have aimed at making frequentist or Baye…

On a Gibbs characterization of normalized generalized Gamma processes

We show that a Gibbs characterization of normalized generalized Gamma processes, recently obtained in Lijoi, Prünster and Walker (2007), can alternatively be derived by exploiting a characterization of exponentially tilted Poisson-Kingman models stated in Pitman (2003). We also provide a completion of this result investigating the existence of normalized random measures inducing exchangeable Gibbs partitions of type $α\in (-\infty, 0]$.

Baysian inference via classes of normalized random measures

One of the main research areas in Bayesian Nonparametrics is the proposal and study of priors which generalize the Dirichlet process. Here we exploit theoretical properties of Poisson random measures in order to provide a comprehensive Bayesian analysis of random probabilities which are obtained by an appropriate normalization. Specifically we achieve explicit and tractable forms of the posterior and the marginal distributions, including an explicit and easily used description of generalizations of the important Blackwell-MacQueen Pólya urn distribution. Such simplifications are achieved by th…

关于归一化逆高斯过程两个被忽视的棍子断裂构造

On two overlooked stick-breaking constructions of the normalized inverse Gaussian process

本文揭示了归一化逆高斯随机离散分布的两种替代棍子断裂构造，分别基于条件布朗运动划分和归一化广义Gamma子序的随机时空变换，并推广到更广泛的分布族。