Asymptotic Bayesian structure learning using graph supports for Gaussian graphical models

TL;DR: In this paper, the authors explore graphical models based on a nonparametric family of distributions, developed from Dirichlet processes, and explore a prior over the graphical model if the random marginals also satisfy the independence constraints.

TL;DR: In this article, a general Markov chain Monte Carlo (MCMC) algorithm is proposed to numerically approximate the posterior distribution on the space of all patterns of mutual independence in a Bayesian framework.

TL;DR: This article proposes a general Markov chain Monte Carlo (MCMC) algorithm to numerically approximate the posterior distribution on the space of all patterns of mutual independence and shows the relationship between such an approach and existing methods in the case of multivariate normal distributions as well as cross-classified multinomial distributions.

TL;DR: In this article, a decomposable graph based partial correlation matrix estimator is proposed for the analysis of time series exhibiting long memory properties, which is derived from the set of wavelet coefficients computed at a given scale; the obtained coefficient are asymptotically uncorrelated.

TL;DR: In this article, a hyper Markov law is defined as a probability distribution over a set of probability measures on a multivariate space that is concentrated on the set of Markov probabilities over some decomposable graph, and satisfies certain conditional independence restrictions related to that graph.

TL;DR: Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided.

TL;DR: In this paper, the authors present a Bayesian data analysis for Bayesian Data Analysis, which is based on Bayesian clustering and Bayesian analysis of Bayesian networks with Bayesian classifiers.