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Many clinical endpoint measures, such as the number of standard drinks consumed per week or the number of days that patients stayed in the hospital, are count data with excessive zeros. However, the zero-inflated nature of such outcomes is…

Identifying which taxa in our microbiota are associated with traits of interest is important for advancing science and health. However, the identification is challenging because the measured vector of taxa counts (by amplicon sequencing) is…

Accurate biodiversity monitoring is essential for effective environmental policy, yet current practices often rely on arbitrarily defined ecosystems, communities, and ad-hoc indicator species, limiting cost-efficiency and reproducibility.…

Accurately identifying spatial patterns of species distribution is crucial for scientific insight and societal benefit, aiding our understanding of species fluctuations. The increasing quantity and quality of ecological datasets present…

The availability of high-throughput parallel methods for sequencing microbial communities is increasing our knowledge of the microbial world at an unprecedented rate. Though most attention has focused on determining lower-bounds on the…

The advances of next-generation sequencing technology have accelerated study of the microbiome and stimulated the high throughput profiling of metagenomes. The large volume of sequenced data has encouraged the rise of various studies for…

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…

Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for…

Monitoring plant and animal populations is an important goal for both academic research and management of natural resources. Successful management of populations often depends on obtaining estimates of their mean or total over a region. The…

Power series distributions form a useful subclass of one-parameter discrete exponential families suitable for modeling count data. A zero-inflated power series distribution is a mixture of a power series distribution and a degenerate…

Inferring microbial interaction networks from abundance patterns is an important approach to advance our understanding of microbial communities in general and the human microbiome in particular. Here we suggest discriminating two levels of…

Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson…

This paper investigates two environmental applications related to climate change, where observations consist of bounded counts. The binomial and beta-binomial (BB) models are commonly used for bounded count data, with the BB model offering…

Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…

We propose a general Bayesian nonparametric (BNP) approach to causal inference in the point treatment setting. The joint distribution of the observed data (outcome, treatment, and confounders) is modeled using an enriched Dirichlet process.…

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 is generally known that counting statistics is not correctly described by a Gaussian approximation. Nevertheless, in neutron scattering, it is common practice to apply this approximation to the counting statistics; also at low counting…

To analyze longitudinal zero-inflated count data, we extend existing models by introducing marginalized zero-inflated Poisson (MZIP) models with random effects, which explicitly capture the marginal effect of covariates and address…

A common approach to analyze a covariate-sample count matrix, an element of which represents how many times a covariate appears in a sample, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency…

Count data with zero inflation and large outliers are ubiquitous in many scientific applications. However, posterior analysis under a standard statistical model, such as Poisson or negative binomial distribution, is sensitive to such…