This question has puzzled me for a long time. I understand the use of 'log' in maximizing the likelihood so I am not asking about 'log'.
My question is, since maximizing log likelihood is equivalent to minimizing "negative log likelihood" (NLL), why did we invent this NLL? Why don't we use the "positive likelihood" all the time? In what circumstances is NLL favored?
I found a little explanation here. https://quantivity.wordpress.com/2011/05/23/why-minimize-negative-log-likelihood/, and it seems to explain the obvious equivalence in depth, but does not solve my confusion.
Any explanation will be appreciated.