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Is there any other reasons beside numerical problems with finite precision system (ieee 754) ? If our computer can have infinite precision, do we still need log likelihood?

Haitao Du
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    https://en.wikipedia.org/wiki/Fisher_information – whuber Aug 14 '16 at 22:56
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    The answer to your other question on why we double the log likelihood (specifically the part of the answer about Wilks' theorem in relation to the likelihood ratio test) would be relevant. – Glen_b Aug 15 '16 at 02:11

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It is not only about the precision but also about efficiency. Log changes the multiplication to summation and the n-th root to division by n which I think makes the computation simpler and faster depending on the formula you are calculating.

Didami
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  • are you saying in assembling language level, multiplication takes more instruction cycles? But we need to pay the price of calculating the log values too, which may take more resource.. – Haitao Du Aug 15 '16 at 13:50
  • I think that didam is right. (+1), taking log transforms products into sums without changing the parameter values that yield a maximum because log is monotonous. The max can be found by taking the derivative which is much easier for sums than for products –  Aug 15 '16 at 14:56