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Frequency school and Bayes school

2022-07-19 03:39:00 elkluh

Frequency school : They think the world is certain . They model directly for the event itself , That is to say, the event tends to a stable value in repeated experiments p, So this value is the probability of the event .

\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)

Bayesian school : They think the world is uncertain , People have a prediction about the world first , And then adjust this prediction through the observation data , Our goal is to find the best probability distribution to describe the world .

\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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