相关论文: Computing all roots of the likelihood equations of…

Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…

Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…

Most statistical software packages implement numerical strategies for computation of maximum likelihood estimates in random effects models. Little is known, however, about the algebraic complexity of this problem. For the one-way layout…

Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying…

Multiple root estimation problems in statistical inference arise in many contexts in the literature. In the context of maximum likelihood estimation, the existence of multiple roots causes uncertainty in the computation of maximum…

In exploratory factor analysis, model parameters are usually estimated by maximum likelihood method. The maximum likelihood estimate is obtained by solving a complicated multivariate algebraic equation. Since the solution to the equation is…

In algebraic statistics, the maximum likelihood degree of a statistical model is the number of complex critical points of its log-likelihood function. A priori knowledge of this number is useful for applying techniques of numerical…

Seemingly unrelated regression models generalize linear regression models by considering multiple regression equations that are linked by contemporaneously correlated disturbances. Robust inference for seemingly unrelated regression models…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as well as special models (e.g. Toeplitz, sparse, trees) that…

Rue and Held (2005) proposed a method for efficiently computing the Gaussian likelihood for stationary Markov random field models, when the data locations fall on a complete regular grid, and the model has no additive error term. The…

In recursive linear models, the multivariate normal joint distribution of all variables exhibits a dependence structure induced by a recursive (or acyclic) system of linear structural equations. These linear models have a long tradition and…

Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…

This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of…

The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…

A local projection model is defined by a set of linear regressions that account for the associations between exogenous variables and an endogenous variable observed at different time points. While it is standard practice to separately…

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…

Correlation matrices are standardized covariance matrices. They form an affine space of symmetric matrices defined by setting the diagonal entries to one. We study the geometry of maximum likelihood estimation for this model and linear…

Gaussian mixture models are central to classical statistics, widely used in the information sciences, and have a rich mathematical structure. We examine their maximum likelihood estimates through the lens of algebraic statistics. The MLE is…

We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…