We are learning this concept in a statistical programming course for research methods, and the professor couldn’t be less clear if he tried. Can someone explain the maximum likelihood estimate (MLE) like I’m five?
In: Mathematics
It’s conceptually pretty simple.
Think of a system that has inputs and outputs. We can see the values of the outputs, but we don’t know what the values of the inputs were.
We want to know what the values of the inputs were.
So we want to figure out what the most likely values of the inputs were.
For every possible set of input values, we figure out how likely that input was to occur. Then we figure out, given that set of input values, how likely the output we got was to happen. We multiply these together to get how likely we were to get that input and then have it produce the output we saw.
Then we pick the input we were most likely to get and have produce the output we saw. That was the most likely input.
An input that was super unlikely to occur, even if it’s likely to produce the output we saw, isn’t a very likely explanation.
Even if an input was likely to occur, if it is super unlikely to produce the output we saw, it isn’t a very likely explanation either.
We want an input that was likely to occur, and likely to produce the output we saw. That’s a likely explanation.
The one that’s the most ( likely to occur * likely to produce the output we saw ) is the most likely explanation.
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