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We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…

We consider the quickest change detection problem where both the parameters of pre- and post- change distributions are unknown, which prevents the use of classical simple hypothesis testing. Without additional assumptions, optimal solutions…

Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…

This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables…

A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…

In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…

This paper considers the problem of estimating a power-law degree distribution of an undirected network using sampled data. Although power-law degree distributions are ubiquitous in nature, the widely used parametric methods for estimating…

In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…

The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As non-parametric model, it offers a very flexible way of modeling…

This paper introduces a new type of probabilistic semiparametric model that takes advantage of data binning to reduce the computational cost of kernel density estimation in nonparametric distributions. Two new conditional probability…

The human microbiome is a complex ecological system, and describing its structure and function under different environmental conditions is important from both basic scientific and medical perspectives. Viewed through a biostatistical lens,…

We describe a general method for the construction of a confidence region for the two parameters of the Negative Binomial Distribution. This is achieved by expanding the sampling distribution of Method-of-Moments estimators, using the…

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…

The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to…

This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the…

The greatest root distribution occurs everywhere in classical multivariate analysis, but even under the null hypothesis the exact distribution has required extensive tables or special purpose software. We describe a simple approximation,…

Consider a setting with multiple units (e.g., individuals, cohorts, geographic locations) and outcomes (e.g., treatments, times, items), where the goal is to learn a multivariate distribution for each unit-outcome entry, such as the…

Zero-inflated regression models have had wide application recently and have provenuseful in modeling data with many zeros. Zero-inflated Binomial (ZIB) regression model is an extension of the ordinary binomial distribution that takes into…

Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…

We explore the class of exchangeable Bernoulli distributions building on their geometrical structure. Exchangeable Bernoulli probability mass functions are points in a convex polytope and we have found analytical expressions for their…