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I am looking at a plot of likelihood against parameters for a Bernoulli context (i.e. finding the p of a coin facing heads) and am comparing it to the equivalent plot for a log likelihood one.

I notice that the peak is a lot sharper for likelihood.

I understand that using log likelihood is a lot easier for us to solve and less computationally expensive, since we are no longer dealing with variables in the power.

Does this mean that we incur a tradeoff of getting a less certain, i.e. higher variance for our estimate?

kjetil b halvorsen
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Ian Petrus Tan
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    There is no inferential difference in using a likelihood or a log-likelihood since they produce exactly the same amount of information. As mentioned, the logarithmic transform is used for computational reasons. – Xi'an Mar 04 '21 at 08:29

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