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A flexible multivariate model for high-dimensional correlated count data

Alexander D. Knudson, Tomasz J. Kozubowski, Anna K. Panorska, A. Grant Schissler
2021 Journal of Statistical Distributions and Applications  
We present basic properties of these mixed Poisson multivariate distributions and provide several examples.  ...  The stochastic rates of the {Yi} are multivariate distributions with arbitrary non-negative margins linked by a copula function.  ...  Bedrick (University of Arizona) for their helpful discussions.  ... 
doi:10.1186/s40488-021-00119-y fatcat:b2hkhyyy3jevlbeelgcw3gcrgm

Discrete Dispersion Models and Their Tweedie Asymptotics [article]

Bent Jørgensen, Célestin C. Kokonendji
2014 arXiv   pre-print
Using the factorial cumulant generating function as tool, we introduce a dilation operation as a discrete analogue of scaling, generalizing binomial thinning.  ...  Many of the results have multivariate analogues, and in particular we consider a class of multivariate Poisson-Tweedie models, a multivariate notion of over- and underdispersion, and a multivariate zero-inflation  ...  An exponential dispersion model ED(µ, γ) with mean µ ∈ Ω, dispersion parameter γ > 0 and unit variance function V (µ) has PDF of the form  ... 
arXiv:1409.7482v1 fatcat:2waw7nex65adhf5cqog6mdsloe

Mixed Poisson Distributions

Dimitris Karlis, Evdokia Xekalaki
2007 International Statistical Review  
Mixed Poisson distributions have been used in a wide range of scientific fields for modeling nonhomogeneous populations.  ...  This paper aims at reviewing the existing literature on Poisson mixtures by bringing together a great number of properties, while, at the same time, providing tangential information on general mixtures  ...  Xekalaki (1986) defined and studied the multivariate generalized Waring distribution, a multivariate mixed Poisson model of this type.  ... 
doi:10.1111/j.1751-5823.2005.tb00250.x fatcat:uv3norbagfb6rhi2ulgaa2jxdi

Generalized Interference Models in Doubly Stochastic Poisson Random Fields for Wideband Communications: the PNSC(alpha) model [article]

Gareth W. Peters, Ido Nevat, Francois Septier, Laurent Clavier
2012 arXiv   pre-print
We develop general parametric density representations for the interference models via doubly stochastic Poisson mixture representations of Scaled Mixture of Normal's via the Normal-Stable variance mixture  ...  The analytic representations obtained are generalizations of Cox processes to the family of sub-exponential models characterized by distributions from the alpha-stable family.  ...  3) point processes; (b) in Lemma 11 we detail analytic distributional representations for the bivariate isotropic stable distribution based on a Scaled Mixture of Normals (representation 1) and an exact  ... 
arXiv:1207.1531v1 fatcat:b3as5dacjzd33ljbfenatvpri4

Page 5345 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
mixtures of distributions.  ...  processes of geometrical objects, shape theory, fibre and surface processes, random tessellations and stereology.  ... 

From here to infinity - sparse finite versus Dirichlet process mixtures in model-based clustering [article]

Sylvia Frühwirth-Schnatter, Gertraud Malsiner-Walli
2018 arXiv   pre-print
Second, sparse finite mixtures are compared to Dirichlet process mixtures with respect to their ability to identify the number of clusters.  ...  A useful concept introduced for Gaussian mixtures by Malsiner Walli et al (2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with K components is chosen  ...  We owe special thanks to Bettina Grün for many helpful comments on preliminary versions of this paper.  ... 
arXiv:1706.07194v3 fatcat:aranerwyfvg5tj5hxhfiizk5su

From here to infinity: sparse finite versus Dirichlet process mixtures in model-based clustering

Sylvia Frühwirth-Schnatter, Gertraud Malsiner-Walli
2018 Advances in Data Analysis and Classification  
(Stat Comput 26:303-324, 2016) are sparse finite mixtures, where the prior distribution on the weight distribution of a mixture with K components is chosen in such a way that a priori the number of clusters  ...  Second, sparse finite mixtures are compared to Dirichlet process mixtures with respect to their ability to identify the number of clusters.  ...  Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution  ... 
doi:10.1007/s11634-018-0329-y pmid:31007770 pmcid:PMC6448299 fatcat:3y2m7vmqrncspm5m7wnivftyda

A (Non‐Central) Chi‐Squared Mixture of Non‐Central Chi‐Squareds is (Non‐Central) Chi‐Squared, and Related Results, Corollaries and Applications

M. C. Jones, Éric Marchand
2021 Stat  
Our main, novel, result is that a certain non-central chi-squared mixture of noncentral chi-squared distributions is itself a scaled non-central chi-squared distribution.  ...  larger than that of the conditional non-central chi-squared distribution, with further consequences pursued.  ...  Consider a classical M/M/1 queueing process with arrivals following a Poisson process with intensity λ and service times occurring independently and identically distributed as exponential with rate µ (  ... 
doi:10.1002/sta4.398 fatcat:kloj2kogyzet3dqsecgsl6rmuq

Semi-parametric modeling of excesses above high multivariate thresholds with censored data

Anne Sabourin
2015 Journal of Multivariate Analysis  
The first issue is tackled using a Poisson process model for extremes, whereas a data augmentation scheme avoids multivariate integration of the Poisson process intensity over both the censored intervals  ...  In this work, a flexible semi-parametric Dirichlet mixture model for angular measures is adapted to the context of censored data and missing components.  ...  The number k of mixture components has truncated geometric distribution, [k] ∝ 1 − 1 λ k−1 1 λ 1 [1,kmax] (k) with upper bound k max = 10 and mean parameter λ = 4.  ... 
doi:10.1016/j.jmva.2015.01.014 fatcat:f2rub6ouzbfvbpaddjuy7yb6ey

Semi-parametric modeling of excesses above high multivariate thresholds with censored data [article]

Anne Sabourin
2014 arXiv   pre-print
The first issue is tackled using a Poisson process model for extremes, whereas a data augmentation scheme avoids multivariate integration of the Poisson process intensity over both the censored intervals  ...  have a parametric distribution.  ...  The number k of mixture components has truncated geometric distribution, [k] ∝ 1 − 1 λ k−1 1 λ 1 [1,kmax] (k) with upper bound k max = 10 and mean parameter λ = 4.  ... 
arXiv:1412.0838v1 fatcat:z4o6beehbbfhdmi26j6hwu4l4a

A mixture model for multivariate extremes

M.-O. Boldi, A. C. Davison
2007 Journal of The Royal Statistical Society Series B-statistical Methodology  
From top to bottom: normal and Poisson with logistic H, normal and Poisson with Dirichlet H, inverted multivariate extreme value distribution and normal dataset.  ...  The Poisson process of vectors is generalized to a Poisson process of measures, the spectral distribution is generalized to the spectral process and its application is illustrated on a real dataset.  ...  The proposal ratio contribution is then 1 because of the symmetry of the normal density.  ... 
doi:10.1111/j.1467-9868.2007.00585.x fatcat:xym6aqm2afbezhvf2uedgfypry

Population counts along elliptical habitat contours: hierarchical modelling using Poisson-lognormal mixtures with nonstationary spatial structure [article]

Alexandra M. Schmidt, Marco A. Rodríguez, Estelina S. Capistrano
2015 arXiv   pre-print
Here, we use hierarchical models based on a Poisson log-normal mixture to understand the spatial variation in relative abundance (counts per standardized unit of effort) of yellow perch, Perca flavescens  ...  Nonstationarity is dealt with using two different approaches, geometric anisotropy, and the inclusion of covariates in the correlation structure of the latent spatial process.  ...  SUPPLEMENTARY MATERIAL Additional results for "Population counts along elliptical habitat contours: hierarchical modelling using Poisson-lognormal mixtures with nonstationary spatial structure" (doi: COMPLETED  ... 
arXiv:1505.04319v1 fatcat:amtksc4ffnahfifvhanrnbvmoy

Bayesian Models for Zero Truncated Count Data

Olumide S. Adesina, Dawud A. Agunbiade, Pelumi E. Oguntunde, Tolulope F. Adesina
2019 Asian Journal of Probability and Statistics  
This study proposed Bayesian multi-level Poisson and Bayesian multi-level Geometric model, Bayesian Monte Carlo Markov Chain Generalized linear Mixed Models (MCMCglmms) of zero truncated Poisson and MCMCglmms  ...  Results obtained showed that Bayesian multi-level Poisson outperformed Bayesian multi-level Poisson Geometric model; also MCMCglmms of zero truncated Poisson outperformed MCMCglmms Poisson.  ...  Acknowledgement The authors appreciate the Medical Director of Ace Medicare Clinics, Ota Ogun state, Nigeria where the data was collected.  ... 
doi:10.9734/ajpas/2019/v4i130105 fatcat:65iiuwzob5hphnvzg3wcji4zgu

Crossbred cow adoption and its correlates: Countable adoption specification search in Sri Lanka's small holder dairy sector

Jagath C. Edirisinghe, Garth J. Holloway
2015 Agricultural Economics  
Reference to the left side of de Finetti's (1938) famous representation theorem motivates Bayesian unification of agricultural adoption studies and facilitates comparisons with conventional binary-choice  ...  Within the binary-choice setting, the probit model is the most celebrated adoption model.  ...  The line of perfect fit is denoted by black dots and the predicted observations derived from the Multivariate-Normal generalization of the Geometric-Beta model are depicted in red.  ... 
doi:10.1111/agec.12195 fatcat:se5syqyta5exjhfx5btxc4zv2m

Risk analysis of animal–vehicle crashes: a hierarchical Bayesian approach to spatial modelling

Andrew Murphy, Jianhong (Cecilia) Xia
2016 International Journal of Crashworthiness  
A hierarchical Bayesian model involving multivariate Poisson lognormal regression is used in establishing the relationship between AVCs and the contributing factors.  ...  A hierarchical Bayesian model involving multivariate Poisson lognormal regression is used in establishing the relationship between AVCs and the contributing factors.  ...  Acknowledgements Thankful to the Department of Main Roads Western Australia for providing the dataset used in the project.  ... 
doi:10.1080/13588265.2016.1209823 fatcat:kngj7l3li5ffja4aei3ddr2e5e
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