相关论文: Objective Bayes testing of Poisson versus inflated…

We developed a statistical theory of zero-count-detector (ZCD), which is defined as a zero-class Poisson under conditions outlined in the paper. ZCD is often encountered in the studies of rare events in physics, health physics, and many…

A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…

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…

The workhorse model for zero-truncated count data (y = 1, 2, ...) is the zero-truncated negative binomial (ZTNB) model. We find it should seldom be used. Instead, we recommend the one-inflated zero-truncated negative binomial (OIZTNB) model…

Many data sets cannot be accurately described by standard probability distributions due to the excess number of zero values present. For example, zero-inflation is prevalent in microbiome data and single-cell RNA sequencing data, which…

This paper proposes a computationally efficient Bayesian factor model for multiple grouped count data. Adopting the link function approach, the proposed model can capture the association within and between the at-risk probabilities and…

This research deals with the estimation and imputation of missing data in longitudinal models with a Poisson response variable inflated with zeros. A methodology is proposed that is based on the use of maximum likelihood, assuming that data…

We consider inventory decisions with many items, each of which has Poisson demand. The rate of demand for individual items is estimated on the basis of observations of past demand. The problem is to determine the items to hold in stock and…

A frequent challenge encountered with compositional ecological data is how to interpret and model data with a high proportion of zeros and $N$'s. Such data frequently occur in ecological applications where counts of species are collected…

Mixed Poisson distributions provide a flexible approach to the analysis of count data with overdispersion, zero inflation, or heavy tails. Since the Poisson mean must be nonnegative, the mixing distribution is typically assumed to have…

We propose a unified probabilistic framework for sparse count tensors with excess zeros, motivated by single-cell Hi-C data. The observed data are naturally represented as a three-way tensor indexed by genomic loci pairs and cells,…

In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…

We consider the problem of comparing two Poisson parameters from the Bayesian perspective. Kawasaki and Miyaoka (2012b) proposed the Bayesian index $P(\lambda_1 < \lambda_2 | X_1,X_2)$ and expressed it using the hypergeometric series. In…

Microorganisms play critical roles in human health and disease. It is well known that microbes live in diverse communities in which they interact synergistically or antagonistically. Thus for estimating microbial associations with clinical…

Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…

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…

This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…

This paper introduces the modeling of circular data with excess zeros under a longitudinal framework, where the response is a circular variable and the covariates can be both linear and circular in nature. In the literature, various…

Weighted networks encode not only the presence of interactions but also their strength. Existing methods for weighted network community detection often rely on Poisson models, which can be restrictive for overdispersed data and make…

In this work we apply the methodology of integral priors to handle Bayesian model selection in binomial regression models with a general link function. These models are very often used to investigate associations and risks in…