Related papers: Dependence on a collection of Poisson random varia…
The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…
Mixture transition distribution time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
A workload model using the infinite source Poisson model for bursts is combined with the on--off model for within burst activity. Burst durations and on--off durations are assumed to have heavy-tailed distributions with infinite variance…
This paper investigates Bayesian variable selection when there is a hierarchical dependence structure on the inclusion of predictors in the model. In particular, we study the type of dependence found in polynomial response surfaces of…
To study the impact of climate variables on morbidity of some diseases in Mexico, we propose a spatio-temporal varying coefficients regression model. For that we introduce a new spatio-temporal dependent process prior, in a Bayesian…
We consider the task of modeling a dependent sequence of random partitions. It is well-known that a random measure in Bayesian nonparametrics induces a distribution over random partitions. The community has therefore assumed that the best…
This article attempts to offer some perspectives on Bayesian inference for finite population quantities when the units in the population are assumed to exhibit complex dependencies. Beginning with an overview of Bayesian hierarchical…
The appropriateness of the Poisson model is frequently challenged when examining spatial count data marked by unbalanced distributions, over-dispersion, or under-dispersion. Moreover, traditional parametric models may inadequately capture…
It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
The current Poisson factor models often assume that the factors are unknown, which overlooks the explanatory potential of certain observable covariates. This study focuses on high dimensional settings, where the number of the count response…
We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is of autoregressive form of order $p$ and is achieved through the use of latent variables. We…
In employing spatial regression models for counts, we usually meet two issues. First, ignoring the inherent collinearity between covariates and the spatial effect would lead to causal inferences. Second, real count data usually reveal over…
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…
Multi-dimensional data frequently occur in many different fields, including risk management, insurance, biology, environmental sciences, and many more. In analyzing multivariate data, it is imperative that the underlying modelling…
We consider Poissonian pair correlations (PPC) for uniformly distributed sequences of random numbers with a dependency structure. More specifically, we treat two classes of dependent random variables which have widely been studied in the…
We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with…
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…
Many application domains such as ecology or genomics have to deal with multivariate non Gaussian observations. A typical example is the joint observation of the respective abundances of a set of species in a series of sites, aiming to…