
Perfect TreeLike Markovian Distributions
We show that if a strictly positive joint probability distribution for a...
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Reading Dependencies from Covariance Graphs
The covariance graph (aka bidirected graph) of a probability distributi...
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Nested Covariance Determinants and Restricted Trek Separation in Gaussian Graphical Models
Directed graphical models specify noisy functional relationships among a...
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On Mean Estimation for Heteroscedastic Random Variables
We study the problem of estimating the common mean μ of n independent sy...
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Characterizations of TwoPoints and Other Related Distributions
We provide new characterizations of twopoints and some related distribu...
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On the symmetric and skewsymmetric Kdistributions
We propose a family of fourparameter distributions that contain the Kd...
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Confidence disc for Cauchy distributions
We will construct a confidence region of parameters for N samples from C...
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Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions
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 normalWishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an n x n, n >= 3, positivedefinite symmetric matrix of random variables and f(W) be a pdf of W. Then, f(W) is a Wishart distribution if and only if W_11W_12W_22^1W_12' is independent of W_12, W_22 for every block partitioning W_11, W_12, W_12', W_22 of W. Similar characterizations of the normal and normalWishart distributions are provided as well. We also show how to construct a prior for every DAG model over X from the prior of a single regression model.
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