Maximum Likelihood Estimation

Updated 04 Oct 2026

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What it is
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  estimates parameters by maximizing the likelihood of the observed data under a specified probabilistic model
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Formula
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  $\hat\theta=\arg\max_\theta L(\theta;\text{data})$ .
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  often maximize the log-likelihood instead, since logarithms preserve the maximizing argument.
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Relationship
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  with independent Gaussian errors of common variance, estimating linear-regression coefficients by maximum likelihood gives the ordinary least-squares coefficients.
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  this equivalence depends on the model assumptions; MLE is not simply another name for least squares.
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Source correction
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  slide 8 of the regression deck repeats the least-squares definition beneath the MLE heading. Replace it with this likelihood-based definition.
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Related
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  Unavailable reference
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  Unavailable reference

Linked references 1