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目前顯示的是 6月, 2017的文章

An Outlier In The Confidence Interval

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In today's department meeting,  I had shared this phenomenon happened in my demo materials for our India customer.  An outlier in the figure is showed as a small red triangle. The blue line just above the outlier is the upper historical limit.  That represents that the outlier is in the historical interval.  The historical interval is like as what we know about the confidence interval.  The historical interval is for a fitted values of the model and has its confidence level 95%. The outlier happened in the historical interval.  There is a little bit conflict with my statistical sense. As our common sense, an outlier is the data out of the range what we expect.  At the same time, about the range what we expect, we in general use the confidence interval to represent.  Intuitively,  an outlier would be out of the interval.  But, in practice, why it is in it? Numerically,  the outlier is detected by the software because its fi...

不變性原則

可能性函式代表一個固定參數的不確定性,但它不是一個機率的密度函式。 那如何處理參數轉換呢?  我們將會假設一個一對一轉換,但這想法能普遍適用。在第一個 binormial 例子中有 n = 10 同時 x = 8,此theta1 = 0.8 vs theta1 = 03 的可能性比為: L( theta1 = 0.8 )      (0.8)^8*(1 - 0.8)^2 -------------------  =  ------------------------- = 208.7 L( theta1 = 0.3 )      (0.3)^8*(1 - 0.3)^2  i.e. 在給定的數據之下,theta 為 0.8 是比 theta 為 0.3 大約多 200 倍的可能。  假設我們對將  theta 表示成 logit 度量有興趣,如:                        theta phi =  log { ------------- } ,                      1 - theta 因此,直覺上我們關於 phi = phi1  = log (0.8/0.2) = 1.39 vs. phi=phi2 = log(0.3/0.7)= -0.85  相對訊息應該是: L*(phi1)       L(theta1) ------------ = -------------= 208.7 L*(phi2)       L(theta2) 那也就是,我們的訊息對參數化(參數轉換)的選取應該是有不變性。 這在貝氏公式並非如此。 假設 theta 有一個無訊息的先驗函式; 後驗函式即為 f(phi|x) = f(th...