Related papers: Variational Estimation for Multidimensional Genera…

In this article, we propose a new method for calculating the mixed correlation coefficient (Pearson, polyserial and polychoric) matrix and its covariance matrix based on the GMM framework. We build moment equations for each coefficient and…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Dynamic Item Response Models extend the standard Item Response Theory (IRT) to capture temporal dynamics in learner ability. While these models have the potential to allow instructional systems to actively monitor the evolution of learner…

Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…

Traditional Item Response Theory models assume the distribution of the abilities of the population in study to be Gaussian. However, this may not always be a reasonable assumption, which motivates the development of more general models.…

We propose a new fiducial Markov Chain Monte Carlo (MCMC) method for fitting parametric Gaussian models. We utilize the Cayley transform to decompose the parametric covariance matrix, which in turn allows us to formulate a general data…

The standard regression tree method applied to observations within clusters poses both methodological and implementation challenges. Effectively leveraging these data requires methods that account for both individual-level and sample-level…

Item Response Theory (IRT) is a powerful statistical approach for evaluating test items and determining test taker abilities through response analysis. An IRT model that better fits the data leads to more accurate latent trait estimates. In…

It is reasonable to consider, in many cases, that individuals' latent traits have a hierarchical structure such that more general traits are a suitable composition of more specific ones. Existing item response models that account for such…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

We consider modeling, inference, and computation for analyzing multivariate binary data. We propose a new model that consists of a low dimensional latent variable component and a sparse graphical component. Our study is motivated by…

This paper introduces a flexible Bayesian nonparametric Item Response Theory (IRT) model, which applies to dichotomous or polytomous item responses, and which can apply to either unidimensional or multidimensional scaling. This is an…

This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models.…

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

We review the literature on algorithms for estimating the index space in a multi-index model. The primary focus is on computationally efficient (polynomial-time) algorithms in Gaussian space, the assumptions under which consistency is…

We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of…

We consider the problem of estimating (diagonally dominant) M-matrices as precision matrices in Gaussian graphical models. These models exhibit intriguing properties, such as the existence of the maximum likelihood estimator with merely two…

We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved…

This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse…