This is notes which I wrote as I was taking video lecture originated from
https://www.youtube.com/watch?v=3S8P3U2ti2A&list=PLbhbGI_ppZISMV4tAWHlytBqNq1-lb8bz&index=70
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What is the Gibbs sampling used for?
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Bayesian network ---> factorization
$$$\alpha, \beta$$$: prior knowledge, constant
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Perform factorization on following plate notation
$$$P(\phi_i;\beta) = P(\phi_i|\beta)P(\beta)$$$
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Graphical model
Factorization using joint
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To make above joint equation simpler, remove $$$\theta$$$ and $$$\phi$$$
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To remove $$$\theta$$$ and $$$\phi$$$, you need to use "marginalize out"
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About $$$\phi$$$
About $$$\theta$$$
2 independant integrations
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So far, you performed following
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What is the $$$\phi$$$?
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What you have done so far?
From (1) and (2), you removed intergrations as much as you could