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enter image description here

thisis the equation of maxilum likelihood

enter image description here

Then this is maximum likelihgood when the distribution is Gaussian distribution.
I want to know to to derive the bottom equation from the left ?

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  • $\begingroup$ Don't post unsearchable images. Instead, typeset your full question (in MathJax). $\endgroup$ Jun 11, 2020 at 5:29

1 Answer 1

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The PDF of the (univariate) normal distribution is

$$\frac{1}{\sigma\sqrt{2\pi}} \exp\left[-\frac{1}{2} \left(\frac{y - \hat{y}}{\sigma}\right)^2\right]$$

This is your $P_{model}(y_i\ | \ x_i ; \theta)$ for a single observation. Assuming each observation is independent, the likelihood (probability of observing $y_1...y_m$ together) is $$\prod_{i = 1}^m P_{model}(y_i\ | \ x_i ; \theta).$$ Taking the log of this whole expression gives your result.

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  • $\begingroup$ can you show some detail? $\endgroup$
    – slowmonk
    Jun 17, 2020 at 5:28
  • $\begingroup$ Is something unclear? I'm not sure what you're confused about $\endgroup$
    – Ben10
    Jun 17, 2020 at 20:19

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