相关论文: Wishart distributions for decomposable graphs
Gaussian covariance graph models encode marginal independence among the components of a multivariate random vector by means of a graph $G$. These models are distinctly different from the traditional concentration graph models (often also…
Let G = An be the graph corresponding to the graphical model of nearest neighbour interaction in a Gaussian character. We study Natural Exponential Families( NEF) ofWishart distributions on convex cones QG and PG, where PG is the cone of…
A complete characterization of Wishart distributions on the cones of positive semi-definite matrices is provided in terms of a description of their maximal parameter domain. This result is new in that also degenerate scale parameters are…
A characterization of the existence of non-central Wishart distributions (with shape and non-centrality parameter) as well as the existence of solutions to Wishart stochastic differential equations (with initial data and drift parameter) in…
We are interested in the distribution of Wishart samples after forgetting their scaling factors. We call such a distribution a projective Wishart distribution. We show that projective Wishart distributions have strong links with the…
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
In this paper, we consider high-dimensional Gaussian graphical models where the true underlying graph is decomposable. A hierarchical $G$-Wishart prior is proposed to conduct a Bayesian inference for the precision matrix and its graph…
In this paper we consider two statistical hypotheses for the families of Wishart type distributions. These distributions are analogs of the Wishart distributions defined and parametrized over a Lorentz cone. We test these hypotheses by…
We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based…
In recent years, a variety of useful extensions of the Wishart have been proposed in the literature for the purposes of studying Markov random fields/graphical models. In particular, generalizations of the Wishart, referred to as Type I and…
In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph $G$. Working with the $W_{P_G}$ family defined by Letac and Massam [Ann. Statist. 35…
In this paper, we consider Gaussian models Markov with respect to an arbitrary DAG. We first construct a family of conjugate priors for the Cholesky parametrization of the covariance matrix of such models. This family has as many shape…
We develop simple methods for constructing parameter priors for model choice among Directed Acyclic Graphical (DAG) models. In particular, we introduce several assumptions that permit the construction of parameter priors for a large number…
Gaussian graphical models have received considerable attention during the past four decades from the statistical and machine learning communities. In Bayesian treatments of this model, the G-Wishart distribution serves as the conjugate…
This paper propose a novel decomposable graphical model to accommodate skew Gaussian graphical models. We encode conditional independence structure among the components of the multivariate closed skew normal random vector by means of a…
In Gaussian graphical models, the zero entries in the precision matrix determine the dependence structure, so estimating that sparse precision matrix and, thereby, learning this underlying structure, is an important and challenging problem.…
The Wishart distribution is the standard conjugate prior for the precision of the multivariate Gaussian likelihood, when the mean is known -- while the normal-Wishart can be used when the mean is also unknown. It is however not so obvious…
Random matrix theory has become a cornerstone in modern statistics and data science, providing fundamental tools for understanding high-dimensional covariance structures. Within this framework, the Wishart matrix plays a central role in…
A recent line of work has studied the relationship between the Wishart matrix $X^\top X$, where $X\in \mathbb{R}^{d\times n}$ has i.i.d. standard Gaussian entries, and the corresponding Gaussian matrix with independent entries above the…
Necessary conditions for the existence of non-central Wishart distributions are given. Our method relies on positivity properties of spherical polynomials on Euclidean Jordan Algebras and advances an approach by Peddada and Richards (1991),…