Related papers: Understanding When Poisson Log-Normal Models Outpe…

Ecological systems are governed by complex interactions which are mainly nonlinear. In order to capture this complexity and nonlinearity, statistical models recently gained popularity. However, although these models are commonly applied in…

This paper introduces a class of generalised linear models (GLMs) driven by latent processes for modelling count, real-valued, binary, and positive continuous time series. Extending earlier latent-process regression frameworks based on…

The advancement of single-cell RNA-sequencing (scRNA-seq) technologies allow us to study the individual level cell-type-specific gene expression networks by direct inference of genes' conditional independence structures. scRNA-seq data…

In this paper, we propose a new Bayesian Poisson network autoregression mixture model (PNARM). Our model combines ideas from the models of Dahl 2008, Ren et al. 2024 and Armillotta and Fokianos 2024, as it is motivated by the following…

The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…

This paper presents a Poisson multi-Bernoulli mixture (PMBM) conjugate prior for multiple extended object filtering. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture…

Poisson-distributed latent variable models are widely used in computational neuroscience, but differentiating through discrete stochastic samples remains challenging. Two approaches address this: Exponential Arrival Time (EAT) simulation…

Marginalized models are in great demand by most researchers in the life sciences particularly in clinical trials, epidemiology, health-economics, surveys and many others since they allow generalization of inference to the entire population…

Bayesian models that can handle both over and under dispersed counts are rare in the literature, perhaps because full probability distributions for dispersed counts are rather difficult to construct. This note takes a first look at Bayesian…

We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…

Penalized regression methods, such as lasso and elastic net, are used in many biomedical applications when simultaneous regression coefficient estimation and variable selection is desired. However, missing data complicates the…

We propose several generalized linear models (GLMs) to predict the number of successful cyber intrusions (or "intrusions") into an organization's computer network, where the rate at which intrusions occur is a function of the following…

Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for…

Overdispersed count data are modelled with likelihood and non-likelihood approaches. Likelihood approaches include the Poisson mixtures with three distributions, the gamma, the lognormal, and the inverse Gaussian distributions.…

The generation of synthetic data with distributions that faithfully emulate the underlying data-generating mechanism holds paramount significance. Wasserstein Generative Adversarial Networks (WGANs) have emerged as a prominent tool for this…

The relationships among ecological variables are usually obtained by fitting statistical models that go through the conditional means of the dependent variables. For example, the nonparametric loess and the parametric piecewise linear…

Modeling count-valued time series has been receiving increasing attention since count time series naturally arise in physical and social domains. Poisson gamma dynamical systems (PGDSs) are newly-developed methods, which can well capture…

We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how…

Markov Chain Monte Carlo (MCMC) algorithms do not scale well for large datasets leading to difficulties in Neural Network posterior sampling. In this paper, we propose Penalty Bayesian Neural Networks - PBNNs, as a new algorithm that allows…

A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand,…