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I'm reading about expectation maximization from Dempster, Laird and Rubin's original paper which can be found from the following link:

http://web.mit.edu/6.435/www/Dempster77.pdf

My questions are from pages 1 and 2. I have added those particular parts into the image below and tried to be as clear as possible with my questions (4 questions in the image, highlighted with red numbers 1, 2, 3, 4). Hope someone could make things clearer for me :)

To summarize my questions in the picture are:

1) Have I understood the relationship between the variables correctly?

2) What does the text in the green box mean exactly?

3) How to interpret these formulas

4) WHAT IS GOING ON HERE?!...this doesn't seem clear at all! x)

enter image description here

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    $\begingroup$ The text clearly states what $g(y|\phi)$ is: a "$\text{family of sampling densities}$", though depending on how you view $\phi$, you could think of it as a conditional density or a family indexed by $\phi$. Why would it be a probability? In 4, $\pi$ is just a parameter there, on which the 4 population probabilities depend. $\endgroup$ – Glen_b Nov 28 '13 at 22:17
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  1. $\mathcal{Y}$: observed $\mathcal{X}$: unobserved In other words,X is the set of latent variables. So, your picture makes sense.

  2. yes!

  3. See, this is just density (probability distribution) which depends on our observations. It doesn't matter what it is (because it can be anything!), what matters is that, this is a function which dependents on our inputs, but it is best represented by f(..|..) which also depends on the latent variables. g(.. | ..) is, the full distribution f(..|..) but with unobserved variables marginalized.
  4. It is referring to Rao(1965)'s work, in which they a have modeled a random process with the given model (with pie and stuff!). I think later they will use this example to demonstrate how their algorithm is working.
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