Difference between revisions of "NeymanPearson中文Spring2014" - Rhea

Revision as of 14:09, 1 May 2014

Hypothesis Testing

PR 的目标是将新的sample进行分类。分类的决定通过假设sample是rv, 其conditional density来自其类别如果知道conditional density， pr的问题就变成statistical hyp testing 的问题如下假设sample属于两个class其中一个、知道conditional density 和 prior

Bayes Decision Rule for Minum Error 假设X是个observation vector. g_i(X) 是X 来自 omega_i 的 Posterior probability Decision rule: 如果个g_1(X) > g_2(X),就选 omega1, 不然选 omega 2 据Bayes theorem, decision rule 可以用likelihood ratio 表示

$\begin{align} & g_1(X) > g_2(X) \\ \Rightarrow & P(\omega_1|X) > P(\omega_2|X) \\ \Rightarrow & \frac{P(X|\omega_1)P(\omega_1)}{P(X)} > \frac{P(X|\omega_2)P(\omega_2)}{P(X)} \\ \Rightarrow & P(X|\omega_1)P(\omega_1) > P(X|\omega_2)P(\omega_2) \end{align}$ Neyman -- Pearson Test

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-Placeholder.  Testing Chinese language input.  尝试中文输入。
+Hypothesis Testing
-*Instructor's comment: I am not sure it's a good idea to put chinese characters in the title of the page. It's probably best to stick with English only for the title of the page. -pm
+PR 的目标是将新的sample进行分类。
-*Page displays ok in my safari browner. -pm
+分类的决定通过
-<math> \theta </math>
+假设sample是rv, 其conditional density来自其类别
+如果知道conditional density， pr的问题就变成statistical hyp testing 的问题
+如下假设sample属于两个class其中一个、知道conditional density 和 prior
+Bayes Decision Rule for Minum Error
+假设X是个observation vector.
+g_i(X) 是X 来自 omega_i 的 Posterior probability
+Decision rule: 如果 个g_1(X) > g_2(X),就选 omega1, 不然选 omega 2
+据Bayes theorem, decision rule 可以用likelihood ratio 表示
+<math>\begin{align}
+&  g_1(X) > g_2(X) \\
+\Rightarrow & P(\omega_1|X) > P(\omega_2|X) \\
+\Rightarrow &  \frac{P(X|\omega_1)P(\omega_1)}{P(X)} > \frac{P(X|\omega_2)P(\omega_2)}{P(X)} \\
+\Rightarrow & P(X|\omega_1)P(\omega_1) > P(X|\omega_2)P(\omega_2)
+\end{align}
+</math>
+Neyman -- Pearson Test

Difference between revisions of "NeymanPearson中文Spring2014" - Rhea

Revision as of 14:09, 1 May 2014

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