A Model for Positively Correlated Count Variables

Jesper Møller and Ege Rubak

International Statistical Review, 2010, vol. 78, issue 1, 65-80

Abstract: An α‐permanental random field is briefly speaking a model for a collection of non‐negative integer valued random variables with positive associations. Though such models possess many appealing probabilistic properties, many statisticians seem unaware of α‐permanental random fields and their potential applications. The purpose of this paper is to summarize useful probabilistic results, study stochastic constructions and simulation techniques, and discuss some examples of α‐permanental random fields. This should provide a useful basis for discussing the statistical aspects in future work. Un champ aléatoire α‐permanental est la modélisation d'une collection de variables aléatoires entières non négatives positivement associées. Malgré leurs attrayantes propriétés probabilistes et leurs nombreuses applications potentielles, ces modèles restent ignorés de la majorité des statisticiens. Le but de cet article est de fournir les résultats probabilistes utiles, d'étudier les constructions stochastiques et les techniques de simulation, ainsi que de discuter quelques exemples, de façon à fournir une base utile à une discussion future des aspects statistiques des champs permanentaux.

Date: 2010
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https://doi.org/10.1111/j.1751-5823.2009.00091.x

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