A priori and posterior likelihood estimation

The prior information of the unknown parameter x  is represented by a distribution form  , which is  called  the prior distribution of the unknown parameter  .

The probability that the result is a cause is the posterior probability.

Likelihood estimation is based on the reason to speculate the probability that the cause will lead to the result.  

 : Indicates the observed data (result)

 : The parameters that determine the data distribution (reasons)

 : Prior   : posterior posterior probability

 : Likelihood estimation

 : evidence Probability statistical information about x.

MLE maximum likelihood estimation:

Maximum posterior estimation:

 

When the maximum posterior and maximum likelihood are optimized, there is a prior term at the time of the maximum posterior  .