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Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

Numerical Analysis · Mathematics 2026-05-12 Josie König , Elizabeth Qian , Melina A. Freitag

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

Machine Learning · Statistics 2024-10-29 Hanwen Huang , Peng Zeng

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…

Statistics Theory · Mathematics 2026-02-02 Partha Sarkar , Kshitij Khare , Malay Ghosh , Matt P. Wand

In Cowell et al. (2007), a Bayesian network for analysis of mixed traces of DNA was presented using gamma distributions for modelling peak sizes in the electropherogram. It was demonstrated that the analysis was sensitive to the choice of a…

Methodology · Statistics 2013-06-21 Therese Graversen , Steffen Lauritzen

There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…

Methodology · Statistics 2018-05-10 Antonio Canale , Daniele Durante , David Dunson

In this paper, we introduce a class of improved estimators for the mean parameter matrix of a multivariate normal distribution with an unknown variance-covariance matrix. In particular, the main results of [D.Ch\'etelat and M. T.…

Statistics Theory · Mathematics 2024-06-25 Arash A. Foroushani , Severien Nkurunziza

For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…

Statistics Theory · Mathematics 2020-09-09 Aziz LMoudden , Éric Marchand

Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…

Methodology · Statistics 2013-03-07 Cinzia Viroli

This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…

Statistics Theory · Mathematics 2008-12-18 Malay Ghosh , Upasana Santra , Dalho Kim

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…

Methodology · Statistics 2021-03-10 Sai Li , Tony T. Cai , Hongzhe Li

Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…

Statistics Theory · Mathematics 2008-05-27 Jiahua Chen , Xianming Tan

We consider the estimation of the mixing distribution of a normal distribution where both the shift and scale are unobserved random variables. We argue that in general, the model is not identifiable. We give an elegant non-constructive…

Statistics Theory · Mathematics 2024-08-20 Ya'acov Ritov

Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…

Applications · Statistics 2011-03-28 Marcos Capistrán , J. Andrés Christen

We consider full Bayesian inference in the multivariate normal mean model in the situation that the mean vector is sparse. The prior distribution on the vector of means is constructed hierarchically by first choosing a collection of nonzero…

Statistics Theory · Mathematics 2012-11-07 Ismaël Castillo , Aad van der Vaart

Given a random sample of observations, mixtures of normal densities are often used to estimate the unknown continuous distribution from which the data come. Here we propose the use of this semiparametric framework for testing symmetry about…

Methodology · Statistics 2012-04-23 Silvia Bacci , Francesco Bartolucci

We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…

Statistics Theory · Mathematics 2022-07-04 Nikolas Siapoutis , Donald Richards , Bharath K. Sriperumbudur

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

Machine Learning · Statistics 2013-02-22 Oren Rippel , Ryan Prescott Adams

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

Methodology · Statistics 2022-10-04 Maoran Xu , Hua Zhou , Yujie Hu , Leo L. Duan

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Methodology · Statistics 2017-02-28 Shonosuke Sugasawa , Tatsuya Kubokawa

This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…

Information Theory · Computer Science 2015-06-03 Jianfeng Yao , Abla Kammoun , Jamal Najim