Related papers: A Bayesian Zero-Inflated Dirichlet-Multinomial Reg…
We consider three new classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. In a previous paper (Bar-Lev and Ridder,…
We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The…
We consider the problem of drawing samples from posterior distributions formed under a Dirichlet prior and a truncated multinomial likelihood, by which we mean a Multinomial likelihood function where we condition on one or more counts being…
Multilevel compositional data are data that are repeatedly measured or clustered within groups and are non-negative and sum to a constant value. These data arise in various settings, such as intensive, longitudinal studies using ecological…
The Nested Dirichlet Distribution (NDD) provides a flexible alternative to the Dirichlet distribution for modeling compositional data, relaxing constraints on component variances and correlations through a hierarchical tree structure. While…
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…
We consider the analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on two alternative modelling approaches: Over-Dispersion (OD) models, and…
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…
Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine.…
Count data are ubiquitous in ecology and the Poisson generalized linear model (GLM) is commonly used to model the association between counts and explanatory variables of interest. When fitting this model to the data, one typically proceeds…
Modern datasets commonly feature both substantial missingness and many variables of mixed data types, which present significant challenges for estimation and inference. Complete case analysis, which proceeds using only the observations with…
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…
We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…
Dirichlet process mixture models (DPMM) play a central role in Bayesian nonparametrics, with applications throughout statistics and machine learning. DPMMs are generally used in clustering problems where the number of clusters is not known…
In this article, we develop a new class of multivariate distributions adapted for count data, called Tree P\'olya Splitting. This class results from the combination of a univariate distribution and singular multivariate distributions along…
Researchers are often interested in predicting outcomes, conducting clustering analysis to detect distinct subgroups of their data, or computing causal treatment effects. Pathological data distributions that exhibit skewness and…
Robustness to distributional shift is one of the key challenges of contemporary machine learning. Attaining such robustness is the goal of distributionally robust optimization, which seeks a solution to an optimization problem that is…
Flexible regression methods where interest centres on the way that the whole distribution of a response vector changes with covariates are very useful in some applications. A recently developed technique in this regard uses the…
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…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…