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Tagged with conditional-independence joint-distribution
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Join distribution of independent random variables that aren't conditionally independent
I am asked to give an example for a joint distribution of three random variables, $U$, $V$ and $W$, where $U$ and $V$ are (unconditionally) independent but are NOT conditionally independent given $W$.
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Distribution of $\max_i \bar{X}-X_i$
Let $X_1, \ldots, X_n$ be i.i.d. random variables from the standard normal distribution and let $\bar{X} = \frac{1}{n}\sum_{i=1}^n X_i$ be their sample mean.
I'm interested in the distribution of the $...
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Joint distribution where random variables always exist in the same orthant
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 ...
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Conditional independence and joint distributions in graphical models
I'm reading Deep Learning by Ian Goodfellow and Yoshua Bengio and Aaron Courville.
In chapter 3 about graphical models, to reduce the model complexity, we assume that certain conditional independence ...
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Joint densities and conditional independece
Let us assume the joint density $p(x,y,z)$ is factorized as $p(y)p(z|y)p(x|z)$. Hence, $x \perp y|z$.
Now, the posterior distribution of z is:
$p(z|x,y)=\frac{p(x,y,z)}{p(x,y)}$, where $p(x,y)=\int p(...
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