Related papers: Extreme sizes in the Gibbs-type exchangeable rando…
We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…
We study measures on random partitions, arising from condensing stochastic particle systems with stationary product distributions. We provide fairly general conditions on the stationary weights, which lead to Poisson-Dirichlet statistics of…
Many popular random partition models, such as the Chinese restaurant process and its two-parameter extension, fall in the class of exchangeable random partitions, and have found wide applicability in model-based clustering, population…
Estimating the number $n$ of unseen species from a $k-$sample displaying only $p\leq k$ distinct sampled species has received attention for long. It requires a model of species abundance together with a sampling model. We start with a…
Asymptotic behaviour of conditional $\alpha$ diversity for the two-parameter Poisson-Dirichlet partition model and for the normalized generalized Gamma model has been recently investigated in Favaro et al. (2009, 2011) with a view to…
We prove a long-standing conjecture which characterises the Ewens-Pitman two-parameter family of exchangeable random partitions, plus a short list of limit and exceptional cases, by the following property: for each $n = 2,3, >...$, if one…
Nonparametric Bayesian approaches to clustering, information retrieval, language modeling and object recognition have recently shown great promise as a new paradigm for unsupervised data analysis. Most contributions have focused on the…
A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of $[n]=\{1,...,n\}$ at time $\theta \ge 0$ is governed by the Ewens sampling formula with parameter $\theta$. These…
Gibbs-type random probability measures, or Gibbs-type priors, are arguably the most "natural" generalization of the celebrated Dirichlet prior. Among them the two parameter Poisson-Dirichlet prior certainly stands out for the mathematical…
Gibbs random fields play an important role in statistics, for example the autologistic model is commonly used to model the spatial distribution of binary variables defined on a lattice. However they are complicated to work with due to an…
Gibbs type priors have been shown to be natural generalizations of Dirichlet process (DP) priors used for intricate applications of Bayesian nonparametric methods. This includes applications to mixture models and to species sampling models…
This article constructs a class of random probability measures based on exponentially and polynomially tilting operated on the laws of completely random measures. The class is proved to be conjugate in that it covers both prior and…
The concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in…
In the language of random counting measures many structural properties of the Poisson process can be studied in arbitrary measurable spaces. We provide a similarly general treatise of Gibbs processes. With the GNZ equations as a definition…
The Ewens-Pitman sampling model (EP-SM) is a distribution for random partitions of the set $\{1,\ldots,n\}$, with $n\in\mathbb{N}$, which is index by real parameters $\alpha$ and $\theta$ such that either $\alpha\in[0,1)$ and…
Generalizations of Bell polynomials, Bell numbers, and Stirling numbers of the second kind have been introduced and their generating functions were evaluated.
This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process.…
We derive explicit Bayesian nonparametric analysis for a species sampling model with finitely many types of Gibbs form of type $\alpha= -1$ recently introduced in Gnedin (2009). Our results complement existing analysis under Gibbs priors of…
We study Gibbs partition models, also known as composition schemes. Our main results comprehensively describe their phase diagram, including a phase transition from the convergent case described in Stufler (2018, Random Structures \&…