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Maximum likelihood estimators

M

matthew levine

Member
I've recently restarted studying after a long break. I can't remember the background to MLEs (or where to find it) and would appreciate a clear, brief summary that explains what they are and why they're useful. I understand the technical process of taking log likelihoods etc., it's more the conceptual understanding that I have (sadly) forgotten from a few years ago.

Any help v. gratefully received!

Thanks,
Matthew
 
I was wrong to discount good old Wikipedia - for anyone else who's similarly puzzled, please note that there are excellent pages if you Google 'Maximum likelihood estimators' and 'likelihood function'.

Matthew
 
MLEs

Matthew,

A PDF gives us the probabilities of a distribution based on certain parameters. For example, we might think that peoples' height is normally distributed with parameters mu and sigma. If we had mu and sigma, we could work out some probabilities from this. But what should mu and sigma be?

This is where MLEs come in. We perform an experiment (eg going out on the street and recording the height of 1000 people) and then ask, what is the best value we can assign to mu and sigma, given this data?

So, a PDF says "what are the probs given the parameters?" A likelihood function says "what are the parameters given the outcome of an experiment?"

Cheers,
John
 
Dear John,

Sorry, I've only just seen your reply from last week. It's very clear (and brief!), so many thanks.

Regards,
Matthew
 
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