[ML] Pretty good tutorial for MLE

What is Maximum Likelihood Estimation (MLE) exactly? This question has bothered me for a long time. When I was reading papers relevant to ICA, the term MLE appeared again. This time, fortunately, I found a really good tutorial in Wikipedia:

Maximum Likelihood Estimation, by S. Purcell.

The first three parts introduce the most fundamental ideas about MLE, and I suggest you, who want to figure out what is MLE, to read these three parts.

In the next three parts, however, some terms and examples seem come from the biology or genetic aspect. If you get confused with the technical words used in ``twin data'', the ``twin study'' item given by Wikipedia might help you.

So far, I've had more clear idea about the difference between the probability and the likelihood estimation, which can be summarized as:

• Probability
• Knowing parameters: Prediction of outcome
• Likelihood
• Observation of data: Estimation of parameters

There still are some concepts I have not quite known yet, such as the ideas presented in the section of ``Likelihood ratio test.''