更改

添加325字节 、 2020年10月28日 (三) 18:10
第148行: 第148行:  
=== Bayes' rule 贝叶斯法则 ===
 
=== Bayes' rule 贝叶斯法则 ===
 
[[Bayes' rule]] for conditional entropy states
 
[[Bayes' rule]] for conditional entropy states
 +
条件熵状态的贝叶斯法则
 +
 +
 
:<math>H(Y|X) \,=\, H(X|Y) - H(X) + H(Y).</math>
 
:<math>H(Y|X) \,=\, H(X|Y) - H(X) + H(Y).</math>
 +
    
''Proof.'' <math>H(Y|X) = H(X,Y) - H(X)</math> and <math>H(X|Y) = H(Y,X) - H(Y)</math>. Symmetry entails <math>H(X,Y) = H(Y,X)</math>. Subtracting the two equations implies Bayes' rule.
 
''Proof.'' <math>H(Y|X) = H(X,Y) - H(X)</math> and <math>H(X|Y) = H(Y,X) - H(Y)</math>. Symmetry entails <math>H(X,Y) = H(Y,X)</math>. Subtracting the two equations implies Bayes' rule.
 +
 +
证明,<math>H(Y|X) = H(X,Y) - H(X)</math> 和 <math>H(X|Y) = H(Y,X) - H(Y)</math>。对称性要求<math>H(X,Y) = H(Y,X)</math>。将两个方程式相减就意味着贝叶斯定律。
 +
 +
    
If <math>Y</math> is [[Conditional independence|conditionally independent]] of <math>Z</math> given <math>X</math> we have:
 
If <math>Y</math> is [[Conditional independence|conditionally independent]] of <math>Z</math> given <math>X</math> we have:
   −
:<math>H(Y|X,Z) \,=\, H(Y|X).</math>
+
如果给定<math>X</math>,<math>Y</math>有条件地独立于<math>Z</math>,则我们有:
       +
:<math>H(Y|X,Z) \,=\, H(Y|X).</math>
    
=== Other properties 其他性质 ===
 
=== Other properties 其他性质 ===
961

个编辑