Multivariate Distributions. Distributions The joint distribution of two random variables is f(x 1,x...
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Transcript of Multivariate Distributions. Distributions The joint distribution of two random variables is f(x 1,x...
![Page 1: Multivariate Distributions. Distributions The joint distribution of two random variables is f(x 1,x 2 ) The marginal distribution of f(x 1 ) is obtained.](https://reader035.fdocuments.in/reader035/viewer/2022062304/56649d765503460f94a5845f/html5/thumbnails/1.jpg)
Multivariate Distributions
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Distributions
• The joint distribution of two random variables is f(x1,x2)
• The marginal distribution of f(x1) is obtained forgetting (integrating) about the values of x2
• The conditional distribution is obtained fixing the value of one of the variables and looking at the other (x1 |x2)
• The variables are independent if
f(x1,x2)= f(x1) f(x2)
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Joint Normal and marginals
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Distributions
• These ideas generalize for any number of variables X=(x1,…xp),
• f(X)=f(x1,…xp), joint
• f(x1,…,xr) si r<p marginal
• f(x1,…,xr |xr+1,…,xk) conditional
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Curse of dimensionality
• The space is vide in high dimensions
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The number of parameters grows faster than the dimension
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• The key variable
N/p (data by dimension)
• At least 10 for inference and if possible 30
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The normal k dimensional
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The normal k dimensional
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proprieties
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propiedades
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Mixtures of distributions
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Mixture distributions
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