The difference between P (X|theta) and P (X;theta)

http://blog.csdn.net/pipisorry/article/details/42715245

Two representations are found when solving maximum likelihood estimates

From:gregor heinrich-parameter estimation for text analysis

from:http://blog.csdn.net/pipisorry/article/details/42649657

There are two ways to represent the reason

P (X|theta) does not always represent conditional probabilities, that is, p (X|theta) does not represent conditional probabilities with P (X;theta) equivalence

And in general

Write the vertical bar to indicate the conditional probability, is a random variable;

The Write semicolon p (x; theta) indicates that the parameter to be evaluated (is fixed, but currently unknown), should be directly considered to be P (x), plus, to illustrate that there is a theta parameter, p (x; theta) means the probability of a random variable x=x. In Bayesian theory, it is called the priori probability of x=x.

Explanation for P (Y|x;theta)

From:andrew ng Machine Learning handout, about presentation methods

For the two representations, the frequency faction and the Bayesian division

The frequency faction thinks that the parameter is a fixed value, refers to the real world, the parameter value is a definite value.

The Bayesian faction thinks that the parameter is a random variable, which means that the value is a certain probability.

from:http://blog.csdn.net/pipisorry/article/details/42715245

The difference between P (X|theta) and P (X;theta)