# Questions tagged [conditional-independence]

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### How to show mathematically whether the following conditional relationships hold?

In the following Bayesian network, the variables $x_{i}$ are mutually independent (let's assume that these are the positions of $N$ boats). The variables $y_{i,j}$ are distance measurements ...
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### Tests with null hypothesis of dependence

Let's say I have a set of variables $\mathbf{V}$ and I want to study conditional dependence between two of them $A, B\in \mathbf{V}$ by conditioning on a set $\mathbf{Z}\subseteq\mathbf{V}$. In other ...
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### Directed graphical models and independence (exercise)

Context: this is Ex. 1 in these notes http://www.stat.cmu.edu/~larry/=sml/DAGs.pdf . The exercise asks to prove that, given a directed graphical model associated to a DAG (directed acyclic graph) $G$: ...
Suppose $X,Y,Z\sim N(0,\sigma^2)$. $X$ is independent of $Y,$ $X$ is independent of $Z$ (but $Y$ and $Z$ are not independent), is $X$ independent of $\max(Y,Z)$?
I am sampling two vectors $x$ and $y$ ($\in \mathbb{R}^n$). First, I sample $x$ from an isotropic Gaussian distribution. Then I want to sample $y$ from the same distribution, but only in the orthant ...