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Bayesian models based on the Dirichlet process and other stick-breaking priors have been proposed as core ingredients for clustering, topic modeling, and other unsupervised learning tasks. Prior specification is, however, relatively…

Methodology · Statistics 2021-10-27 Ryan Giordano , Runjing Liu , Michael I. Jordan , Tamara Broderick

Bayesian models based on the Dirichlet process and other stick-breaking priors have been proposed as core ingredients for clustering, topic modeling, and other unsupervised learning tasks. However, due to the flexibility of these models,…

Methodology · Statistics 2022-01-27 Ryan Giordano , Runjing Liu , Michael I. Jordan , Tamara Broderick

We consider Bayesian nonparametric density estimation using a Pitman-Yor or a normalized inverse-Gaussian process kernel mixture as the prior distribution for a density. The procedure is studied from a frequentist perspective. Using the…

Statistics Theory · Mathematics 2013-02-15 Catia Scricciolo

The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke different spiking patterns at each trial. Probabilistic methods are essential to understand the functional role of this variance within…

Neurons and Cognition · Quantitative Biology 2016-11-15 Wahiba Taouali , Giacomo Benvenuti , Pascal Wallisch , Frédéric Chavane , Laurent Perrinet

This paper introduces a discrete-time fractional Poisson process defined as a renewal process, where the waiting times follow a discrete Mittag-Leffler distribution. We investigate its fundamental properties by explicitly deriving the…

Probability · Mathematics 2026-05-06 Naohiro Yoshida

The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed…

Optimization and Control · Mathematics 2021-01-12 Krzysztof J. Szajowski

We introduce a family of multiscale stick-breaking mixture models for Bayesian nonparametric density estimation. The Bayesian nonparametric literature is dominated by single scale methods, exception made for P\`olya trees and allied…

Methodology · Statistics 2020-01-17 Marco Stefanucci , Antonio Canale

We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying…

Statistics Theory · Mathematics 2012-04-20 John Paisley , David Blei , Michael I. Jordan

We discuss species distribution models (SDM) for biodiversity studies in ecology. SDM plays an important role to estimate abundance of a species based on environmental variables that are closely related with the habitat of the species. The…

Applications · Statistics 2023-05-01 Osamu Komori , Yusuke Saigusa , Shinto Eguchi

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and…

Statistics Theory · Mathematics 2013-09-03 Jeffrey W. Miller , Matthew T. Harrison

An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of…

Astrophysics · Physics 2007-05-23 Juergen Prahl

We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…

Statistics Theory · Mathematics 2014-09-29 Bent Jørgensen , Célestin C. Kokonendji

Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of the individual…

Disordered Systems and Neural Networks · Physics 2007-05-23 Thierry Huillet

There is a growing interest in learning how the distribution of a response variable changes with a set of predictors. Bayesian nonparametric dependent mixture models provide a flexible approach to address this goal. However, several…

Computation · Statistics 2020-05-06 Tommaso Rigon , Daniele Durante

A new class of nonparametric prior distributions, termed Beta-Binomial stick-breaking process, is proposed. By allowing the underlying length random variables to be dependent through a Beta marginals Markov chain, an appealing discrete…

Statistics Theory · Mathematics 2020-08-12 María F. Gil-Leyva , Ramsés H. Mena , Theodoros Nicoleris

The Poisson--Dirichlet distribution arises in many different areas. The parameter $\theta$ in the distribution is the scaled mutation rate of a population in the context of population genetics. The limiting case of $\theta$ approaching…

Probability · Mathematics 2008-11-12 Shui Feng , Fuqing Gao

We exploit a suitable moment-based characterization of the mixture of Poisson distribution for developing Bayesian inference for the unknown size of a finite population whose units are subject to multiple occurrences during an enumeration…

Methodology · Statistics 2018-06-19 Danilo Alunni Fegatelli , Luca Tardella

In this paper, two parametric probability distributions capable to describe the statistics of X-ray photon detection by a CCD are presented. They are formulated from simple models that account for the pile-up phenomenon, in which two or…

Instrumentation and Methods for Astrophysics · Physics 2013-10-30 Diego J. R. Sevilla

Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Indeed, many popular nonparametric priors, such as…

Statistics Theory · Mathematics 2015-03-03 P. De Blasi , S. Favaro , A. Lijoi , R. H. Mena , I. Pruenster , M. Ruggiero

Poisson-like behavior for event count data is ubiquitous in nature. At the same time, differencing of such counts arises in the course of data processing in a variety of areas of application. As a result, the Skellam distribution -- defined…

Probability · Mathematics 2018-04-04 H. L. Gan , Eric D. Kolaczyk