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I was reading in "Using Maximum Likelihood Estimation" from "Econometrics for Dummies", and here's what the author had to say: "The objective of maximum likelihood (ML) estimation is to choose values for the estimated parameters (betas) that would maximize the probability of observing the Y values in the sample with the given X values. This probability is summarized in what is called the likelihood function. " (Source: http://www.dummies.com/how-to/content/using-maximum-likelihood-ml-estimation.html)

He seems to be saying that we want to find the parameters that make Y most likely to occur given an X value, but I thought the objective might be to find the parameters that most likely reveal the true P(Y|X).

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Oh, I think I understand a bit better now. The objective is to find parameters that maximize the likelihood that our observations will be similar if we take another, similar, sample. For example, let's say that we draw 5 marbles from a bag and 3 of them are black. We then place them back in the bag. Our objective, then, is to figure out the fraction of black marbles in the bag that would make us most likely to see 3 black marbles the next time we draw 5.

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