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By resorting to sequential constructions of exchangeable random partitions (Pitman, 2006), and exploiting some known facts about generalized Stirling numbers, we derive a generalized Chinese restaurant process construction of exchangeable…

Probability · Mathematics 2008-05-27 Annalisa Cerquetti

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…

Methodology · Statistics 2017-11-21 Giuseppe Di Benedetto , François Caron , Yee Whye Teh

This work is devoted to the analysis of a Gibbs partition model, also known as a composition scheme. We consider a natural new condition on the component weights. It leads to a new behavior for the total number of components. We discover a…

Combinatorics · Mathematics 2025-09-29 Niccolò Bosio , Markus Kuba , Benedikt Stufler

The infinitely-many-neutral-alleles model has recently been extended to a class of diffusion processes associated with Gibbs partitions of two-parameter Poisson-Dirichlet type. This paper introduces a family of infinite-dimensional…

Probability · Mathematics 2013-02-15 Matteo Ruggiero , Stephen G. Walker , Stefano Favaro

In mathematical finance, Levy processes are widely used for their ability to model both continuous variation and abrupt, discontinuous jumps. These jumps are practically relevant, so reliable inference on the feature that controls jump…

Statistics Theory · Mathematics 2021-09-21 Zhe Wang , Ryan Martin

One of the most used priors in Bayesian clustering is the Dirichlet prior. It can be expressed as a Chinese Restaurant Process. This process allows nonparametric estimation of the number of clusters when partitioning datasets. Its key…

Machine Learning · Computer Science 2021-04-27 Gaël Poux-Médard , Julien Velcin , Sabine Loudcher

Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of…

Statistics Theory · Mathematics 2024-05-31 Louise Alamichel , Daria Bystrova , Julyan Arbel , Guillaume Kon Kam King

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…

Probability · Mathematics 2024-01-09 Steffen Betsch

We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…

Combinatorics · Mathematics 2020-04-01 Benedikt Stufler

We place an Indian Buffet process (IBP) prior over the structure of a Bayesian Neural Network (BNN), thus allowing the complexity of the BNN to increase and decrease automatically. We further extend this model such that the prior on the…

Machine Learning · Statistics 2021-08-03 Samuel Kessler , Vu Nguyen , Stefan Zohren , Stephen Roberts

We show that a Gibbs characterization of normalized generalized Gamma processes, recently obtained in Lijoi, Pr\"unster and Walker (2007), can alternatively be derived by exploiting a characterization of exponentially tilted Poisson-Kingman…

Probability · Mathematics 2010-01-02 Annalisa Cerquetti

The Pitman-Yor process is a random discrete probability distribution of which the atoms can be used to model the relative abundance of species. The process is indexed by a type parameter $\sigma$, which controls the number of different…

Statistics Theory · Mathematics 2022-08-31 S. E. M. P. Franssen , A. W. van der Vaart

Analyzing multivariate time series data is important to predict future events and changes of complex systems in finance, manufacturing, and administrative decisions. The expressiveness power of Gaussian Process (GP) regression methods has…

Machine Learning · Statistics 2019-05-23 Anh Tong , Jaesik Choi

In this paper we consider a Bayesian framework for making inferences about dynamical systems from ergodic observations. The proposed Bayesian procedure is based on the Gibbs posterior, a decision theoretic generalization of standard…

Statistics Theory · Mathematics 2019-01-28 Kevin McGoff , Sayan Mukherjee , Andrew Nobel

There is a very rich literature proposing Bayesian approaches for clustering starting with a prior probability distribution on partitions. Most approaches assume exchangeability, leading to simple representations in terms of Exchangeable…

Methodology · Statistics 2021-02-02 Sally Paganin , Amy H. Herring , Andrew F. Olshan , David B. Dunson

The hierarchical Dirichlet process is the cornerstone of Bayesian nonparametric multilevel models. Its generative model can be described through a set of latent variables, commonly referred to as tables within the popular restaurant…

Statistics Theory · Mathematics 2025-05-06 Marta Catalano , Claudio Del Sole

Factor Analysis has traditionally been utilized across diverse disciplines to extrapolate latent traits that influence the behavior of multivariate observed variables. Historically, the focus has been on analyzing data from a single study,…

Methodology · Statistics 2026-01-22 Elena Bortolato , Antonio Canale

Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we…

Probability · Mathematics 2013-09-06 Stefano Favaro , Antonio Lijoi , Igor Prünster

Gibbs sampling from continuous real-valued functions is a challenging problem of interest in machine learning. Here we leverage quantum Fourier transforms to build a quantum algorithm for this task when the function is periodic. We use the…

Quantum Physics · Physics 2024-07-23 Arsalan Motamedi , Pooya Ronagh

We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…

Methodology · Statistics 2007-10-24 Omiros Papaspiliopoulos , Gareth Roberts