R Statistics Cookbook

Maximum likelihood estimation

Suppose we observe a hundred roulette spins, and we get red 30 times and black 70 times. We can start by assuming that the probability of getting red is 0.5 (and black is obviously 0.5). This is certainly not a very good idea, because if that was the case, we should have seen nearly red 50 times and black 50 times, but we did not. It is thus evident that a more reasonable assumption would have been a probability of 0.3 for red (and thus 0.7 for black).

The principle of maximum likelihood establishes that, given the data, we can formulate a model and tweak its parameters to maximize the probability (likelihood) of having observed what we did observe. Additionally, maximum likelihood allows us to calculate the ...