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→Bayes' rule 贝叶斯法则
=== 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:
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 ===