Related papers: Maximum Likelihood Estimates for Gaussian Mixtures…
We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and…
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in…
This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent…
We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
Flexible random scale-mixture models provide a framework for capturing a broad range of extremal dependence structures. However, likelihood-based inference under the peaks-over-threshold setting is often computationally infeasible, due to…
A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There…
We explore the maximum likelihood degree of a homogeneous polynomial $F$ on a projective variety $X$, $\mathrm{MLD}_F(X)$, which generalizes the concept of Gaussian maximum likelihood degree. We show that $\mathrm{MLD}_F(X)$ is equal to the…
Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the…
The field of extreme value statistics is concerned with modeling and predicting rare events. In a H\"usler-Reiss graphical model, a graph represents extremal conditional independence (CI) relations between random variables. These models are…
We study approximation methods for a large class of mixed models with a probit link function that includes mixed versions of the binomial model, the multinomial model, and generalized survival models. The class of models is special because…
Mixtures of Gaussian Bayesian networks have previously been studied under full-covariance assumptions, where each mixture component has its own covariance matrix. We propose a mixture model with tied-covariance, in which all components…
This note aims to demonstrate that performing maximum-likelihood estimation for a mixture model is equivalent to minimizing over the parameters an optimal transport problem with entropic regularization. The objective is pedagogical: we seek…
Maximum likelihood estimation is a fundamental optimization problem in statistics. We study this problem on manifolds of matrices with bounded rank. These represent mixtures of distributions of two independent discrete random variables. We…
In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…
In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no…
Principal stratification is a widely used framework for addressing post-randomization complications. After using principal stratification to define causal effects of interest, researchers are increasingly turning to finite mixture models to…
In this letter we generalise Ensemble Kalman inversion techniques to general Bayesian models where previously they were restricted to additive Gaussian likelihoods - all in the difficult setting where the likelihood can be sampled from, but…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…