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In statistics one often hears the phrases "log likelihood" and "log error". Why is it natural to consider the logarithm of these guys? My wild guess is that the Gaussian is a pretty "normal" distribution, and it's natural to take the log of such a thing. But this is pretty sketchy.

A pointer to a reference would be great.

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Why does someone think this question is off-topic, I wonder? It would also be on topic on stats.SE, but that doesn't make it unwanted here. – Henning Makholm Feb 5 '13 at 21:42
it is like you wanna marry a beautiful girl and to get her is very difficult.. however her mother is easier to convince and you also know that the girl you love always listens to her mother. What is the best strategy? first to get the mothers mind and eventually you will get the girl.. other way around is difficult.. now what is log? – Seyhmus Güngören Feb 5 '13 at 23:40
up vote 1 down vote accepted

Motivation: It's just easier to work with log-likelihood sometimes (e.g. if the likelihood is an exponential function).

Justification: Since log is an increasing function, whatever maximises log-likelihood also maximises likelihood.

Wikipedia on Log-likelihood

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