Perfect Tree-Like Markovian Distributions

by   Ann Becker, et al.

We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations enclosed in the distribution. The same result is shown to hold also for multivariate strictly positive normal distributions. Our proof uses a new property of conditional independence that holds for these two classes of probability distributions.


page 1

page 2

page 3

page 4


No eleventh conditional Ingleton inequality

A rational probability distribution on four binary random variables X, Y...

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 t...

On Testing Whether an Embedded Bayesian Network Represents a Probability Model

Testing the validity of probabilistic models containing unmeasured (hidd...

Determining full conditional independence by low-order conditioning

A concentration graph associated with a random vector is an undirected g...

Diagonal Nonlinear Transformations Preserve Structure in Covariance and Precision Matrices

For a multivariate normal distribution, the sparsity of the covariance a...

Safe Probability

We formalize the idea of probability distributions that lead to reliable...

Equilibrium Points of an AND-OR Tree: under Constraints on Probability

We study a probability distribution d on the truth assignments to a unif...

Please sign up or login with your details

Forgot password? Click here to reset