Related papers: On the Behrens--Fisher problem: A globally converg…
Logistic regression involving high-dimensional covariates is a practically important problem. Often the goal is variable selection, i.e., determining which few of the many covariates are associated with the binary response. Unfortunately,…
The von Mises-Fisher distribution is one of the most widely used probability distributions to describe directional data. Finite mixtures of von Mises-Fisher distributions have found numerous applications. However, the likelihood function…
The likelihood ratio (LR) is largely used to evaluate the relative weight of forensic data regarding two hypotheses and for its assessment Bayesian methods are widespread in the forensic field. However, the Bayesian `recipe' for the LR…
Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally…
Robust estimators and Wald-type tests are developed for the multinomial logistic regression based on $\phi$-divergence measures. The robustness of the proposed estimators and tests is proved through the study of their influence functions…
Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log--likelihood function of two unknown densities is of some parametric form. The model has been…
We propose a new test to address the nonparametric Behrens-Fisher problem involving different distribution functions in the two samples. Our procedure tests the null hypothesis $\mathcal{H}_0: \theta = \frac{1}{2}$, where $\theta = P(X<Y) +…
In this paper we deal with the problem of sequential testing of multiple hypotheses. The main goal is minimizing the expected sample size (ESS) under restrictions on the error probabilities. We take, as a criterion of minimization, a…
The paper analyzes theoretically and empirically the performance of likelihood weighting (LW) on a subset of nodes in Bayesian networks. The proposed scheme requires fewer samples to converge due to reduction in sampling variance. The…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
We consider the branch-length estimation problem on a bifurcating tree: a character evolves along the edges of a binary tree according to a two-state symmetric Markov process, and we seek to recover the edge transition probabilities from…
We study the convergence behavior of the Expectation Maximization (EM) algorithm on Gaussian mixture models with an arbitrary number of mixture components and mixing weights. We show that as long as the means of the components are separated…
Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…
A new multivariate integer-valued Generalized AutoRegressive Conditional Heteroscedastic process based on a multivariate Poisson generalized inverse Gaussian distribution is proposed. The estimation of parameters of the proposed…
We study stochastic optimization problems with objective function given by the expectation of the maximum of two linear functions defined on the component random variables of a multivariate Gaussian distribution. We consider random…
A systematic approach to finding variational approximation in an otherwise intractable non-conjugate model is to exploit the general principle of convex duality by minorizing the marginal likelihood that renders the problem tractable. While…
The Behrens-Fisher Problem is a classical statistical problem. It is to test the equality of the means of two normal populations using two independent samples, when the equality of the population variances is unknown. Linnik (1968) has…
We propose a novel Bregman descent algorithm for minimizing a convex function that is expressed as the sum of a differentiable part (defined over an open set) and a possibly nonsmooth term. The approach, referred to as the Variable Bregman…
The problem of testing the equality of mean vectors for high-dimensional data has been intensively investigated in the literature. However, most of the existing tests impose strong assumptions on the underlying group covariance matrices…
Computing the exact likelihood of data in large Bayesian networks consisting of thousands of vertices is often a difficult task. When these models contain many deterministic conditional probability tables and when the observed values are…