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We develop tools for selective inference in the setting of group sparsity, including the construction of confidence intervals and p-values for testing selected groups of variables. Our main technical result gives the precise distribution of…

Inference of the marginal probability distribution is defined as the calculation of the probability of a subset of the variables and is relevant for handling missing data and hidden variables. While inference of the marginal probability…

Over the past decade network theory has been applied successfully to the study of a variety of complex adaptive systems. However, the application of these techniques to non-human social networks has several shortfalls. Firstly, in most…

Food authenticity studies are concerned with determining if food samples have been correctly labeled or not. Discriminant analysis methods are an integral part of the methodology for food authentication. Motivated by food authenticity…

Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…

Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale…

Codifference is a commonly used measure of dependence for stable vectors and processes for which covariance is infinite. However, we argue that it can also be used for other heavy-tail distributions and it provides useful information for…

A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…

The "large p, small n" paradigm arises in microarray studies, where expression levels of thousands of genes are monitored for a small number of subjects. There has been an increasing demand for study of asymptotics for the various…

The multivariate extremal index function relates the asymptotic distribution of the vector of pointwise maxima of a multivariate stationary sequence to that of the independent sequence from the same stationary distribution. It also measures…

Many important problems in psychology and biomedical studies require testing for overdispersion, correlation and heterogeneity in mixed effects and latent variable models, and score tests are particularly useful for this purpose. But the…

Assessing model generalization under distribution shift is essential for real-world deployment, particularly when labeled test data is unavailable. This paper presents a unified and practical framework for unsupervised model evaluation and…

With the development of next generation sequencing technology, researchers have now been able to study the microbiome composition using direct sequencing, whose output are bacterial taxa counts for each microbiome sample. One goal of…

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…

Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…

Codispersion analysis is a new statistical method developed to assess spatial covariation between two spatial processes that may not be isotropic or stationary. Its application to anisotropic ecological datasets have provided new insights…

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.…

Outlying observations are frequently encountered across a wide spectrum of scientific domains, posing notable challenges to the generalizability of statistical models and the reproducibility of downstream analysis. They are identified…

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…

Using a sample from a population to estimate the proportion of the population with a certain category label is a broadly important problem. In the context of microbiome studies, this problem arises when researchers wish to use a sample from…