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"maximum likelihood" is a grammatically correct phrase and can be used in written English.
It is a statistical concept usually used in scientific and financial texts. For example: "The parameters of the model were estimated using maximum likelihood methods."
Exact(60)
maximum likelihood linear regression.
Maximum likelihood estimation detector.
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robust maximum likelihood estimator.
maximum likelihood detection.
maximum likelihood expectation maximization.
maximum likelihood ratio test.
restricted maximum likelihood approach.
Statistical Method: Maximum Likelihood.
full information maximum likelihood.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com