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Frequency school and Bayes school

2022-07-19 03:39:00 【elkluh】

$\theta$ Is an unknown constant , x Is a randomly distributed variable .

x_i $\underset{\sim}{iid}$ $p(x|\theta)$

$p(x|\theta)=\prod_{i=1}^Np(x_i|\theta)$

MLE( Maximum likelihood estimation ,Maximum likelihood estimation）： Estimated make p maximal $\theta$

$\theta_{MLE} = arg\underset{\theta}{max}\log(p|\theta)$

$\theta$ Is a random variable , $\theta \sim \ p(\theta)$

Bayes theorem ： $p(\theta|x) = \frac{p(x|\theta)p(\theta)}{p(x)}$

MAP( Maximum posterior estimate ,Maximum A posteriori)

$\theta_{MAP} = argmax\ p(\theta|x) = arg \underset{\theta}{max}\ p(x|\theta)p(\theta)$

Prior probability ： The probability of predicting what an event is before you know what it is

Posterior probability ： I know what the event is , To guess the probability of the occurrence of the event .

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