Understanding of prior probability, posterior probability and Bayesian formula

Catalog

1、 Conditional probability

2、 All probability formula

3、 Prior probability

4、 Posterior probability

5、 Bayes （bayes） The formula

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Before introducing these concepts , The first thing to understand is   Conditional probability   And   All probability formula  .

1、 Conditional probability

In the event B What happened under the conditions A Probability of occurrence .

P(AB) by A、B Probability of simultaneous occurrence , In the case of independent and identically distributed P(AB)=P(A)P(B).

2、 All probability formula

If things A There may be B1、B2… Many reasons lead to , be

  The test is E A partition of sample space ,A The test is E Events .

3、 Prior probability

Known based on previous experience or data analysis （ reason 、 Category 、 Way, etc ） probability .

4、 Posterior probability

If the prior probability is P(A) , said P(A|b) by Posterior probability , Or get b The probability calculated after the information of , Judge the result （b） What is the reason for the occurrence of （A） The probability of causing . A posteriori probability means a bit of hindsight , I'll find the cause of this event after it happened .

5、 Bayes （bayes） The formula

Bayes' formula Is a way to calculate the posterior probability , The formula is as follows

Bayes' formula It is mainly used when an event is observed （b） When it has happened , Find out the various reasons that led to this event 、 situation 、 The likelihood of the type of path or event . Used in the formula P(b|A) Referred to as Class conditional probability , That is to get the probability of something happening from the reason .

for example , In the field of machine learning , if b It's a picture , hold b As input to the network , be Posterior probability P(A|b) It can be used as b Belong to the category A Probability .