I am having the following problem:
Consider variables $X_1, X_2, X_3$ with joint normal distribution with standard normal margins which are equicorrelated (all correlations are equal to$\rho \in (0,1)$). \textbf{Is it possible to represent the dependence structure of these varriables with mixture of three Markov tree distributions?}
So I think it is not possible if you have one markov tree because observing the random variable, we see that X_1 and X_3 are conditional independent given X_2. With some linear algebra we have $\rho_{13}=\rho_{12}\rho_{23}$. So we can get $\rho=\rho^2$ always unless $\rho=0$ or $1$.
I dont know how to continue from here. Any tip is appreciated.