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We initiate the study of proper losses for evaluating generative models in the discrete setting. Unlike traditional proper losses, we treat both the generative model and the target distribution as black-boxes, only assuming ability to draw…

Count data are common in medical research. When these data have more zeros than expected by the most used count distributions, it is common to employ a zero-inflated regression model. However, the interpretability of these models is much…

We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses…

We propose a general method for distributed Bayesian model choice, using the marginal likelihood, where a data set is split in non-overlapping subsets. These subsets are only accessed locally by individual workers and no data is shared…

We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce…

With nonignorable missing data, likelihood-based inference should be based on the joint distribution of the study variables and their missingness indicators. These joint models cannot be estimated from the data alone, thus requiring the…

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…

Diffusion models have recently emerged as powerful tools for missing data imputation by modeling the joint distribution of observed and unobserved variables. However, existing methods, typically based on stochastic denoising diffusion…

We propose nonparametric identification and semiparametric estimation of joint potential outcome distributions in the presence of confounding. First, in settings with observed confounding, we derive tighter, covariate-informed bounds on the…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…

The Bell regression model (BRM) is a statistical model that is often used in the analysis of count data that exhibits overdispersion. In this study, we propose a Bayesian analysis of the BRM and offer a new perspective on its application.…

Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…

Conducting valid statistical analyses is challenging in the presence of missing-not-at-random (MNAR) data, where the missingness mechanism is dependent on the missing values themselves even conditioned on the observed data. Here, we…

Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be…

An extensive body of literature exists that specifically addresses the univariate case of zero-inflated count models. In contrast, research pertaining to multivariate models is notably less developed. We proposed two new parsimonious…

Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior…

Consider a multinomial regression model where the response, which indicates a unit's membership in one of several possible unordered classes, is associated with a set of predictor variables. Such models typically involve a matrix of…

The paper investigates a discrete time Binomial risk model with different types of polices and shock events may influence some of the claim sizes. It is shown that this model can be considered as a particular case of the classical compound…

Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to…

Data analyses typically rely upon assumptions about missingness mechanisms that lead to observed versus missing data. When the data are missing not at random, direct assumptions about the missingness mechanism, and indirect assumptions…