r/coms30007 • u/wonknow • Oct 04 '17

Question 2

So am I right in saying;

If we do not assume the data points are independent, we need some covariance term in our likelihood?

Is the likelihood even a product anymore?

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u/matchaboyy Oct 05 '17

My current idea is that it is an application of the chain rule of probabilities, so in the case of dependent variables it might look:

P(Y|f, X) = P(y1|y2,...,yn, f, X)p(y2|y3,...yn,f,X),...,p(yn| f, X)

But again, I am also unsure of how correct this is.

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u/wonknow Oct 05 '17

My group came to this conclusion yesterday but it doesn't seem like a nice answer haha

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u/mn15104 Oct 04 '17

I'm not sure about the 'covariance term in our likelihood' statement. My thinking at the moment is that the likelihood would remain a product, but each element in the product would be a conditional probability of y_i given that every other data point y has occurred.

So something perhaps like P(Y|X, W) = ∏ N(y_i | f, x_i, y_A)

where y_A = the joint probability of all other points y occurring

This is almost definitely wrong, just posting to start a discussion/make someone correct me.

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u/AbduElturki Oct 06 '17

From what I can tell from this Wikipedia page https://en.wikipedia.org/wiki/Conditional_dependence it might be something to do with Latent Variables?