Re: [計算] signal-detection的計算
印象中有回過, 卻找不到...
前兩天太累了, 可能回到一半就放棄或者因中斷而被清掉?
※ 引述《yuu0826.bbs@ptt.cc (要來唸請慎重考慮)》之銘言：
> 其實我不知道該去哪裡問...因為是實驗法的題目
> 好像又不屬於統計的範疇@@" 而且看到指數對數就很頭痛 >//////<
你沒學過統計?
那要怎麼講?
> 所以想請教大家 給我一些指引 :)
> Suppose a gang of smugglers were trying illegally to export radioactive
> material.In an effort to try to stop this, you monitor with a Geiger
> counter every package leaving the country.
> For those packages without the radioactive material (NRA)
> the number of counts is given approximately by an exponential
> distribution.
> Letting x equal the number of counts:
> f(x|NRA) = λe^(-x)
"f" 是甚麼? p.d.f.? 那怎會有 "λ"?
> For the package with radio active material (RA)
> f(x|RA) = λe^(-λx) 0 < λ < 1.00
> (a) What is the likelihood ratio of a package’s containing radioactive
> material as opposed to its not containing radioactive material?
"likelihood ratio" 是甚麼?
不知道的話去看看 mathematical statistics 的教本吧!
> (b) If the a priori probability of a package’s containing radioactive
> material is 1 in 10^6 , and if
> $100 is cost of opening a package and repacking it if does not contain
> radioactive material (false alarm -$100)
> $10^4 is value of catching a radioactive package (Hit +$10^4)
> $10^6 is cost of letting a radioactive package through (Miss -$10^6)
> $0 is the value of letting a nonradioactive package through
> (correct rejection +$0)
> What value of likelihood ratio should lead one to ask that the package
> be opened?
其實這題目的假設有問題.
設定上參數 λ 在 0-1 之間, 不含 0.
那麼 prior 設定 P[0<λ<1] = 1/10^6, 要如何去處理不
同 λ 值的問題?
既然在 prior 及報酬函數都只考慮 simple vs. simple
的檢定問題, 就應設定單一 λ 值.
> (c) If =1/6, what value of x would one need to attain that value of
> likelihood ratio in (b)?
在 simple vs. simple 假說檢定問題,這小題只不過是把
概度比表示的棄卻域變成用 x 表示罷了!
只是, 題目卻設定非單一的 λ 值...
> Suppose your budge director gives you $300,000 per year, so that you can
> afford to open 3000 packages per year even if none is radioactive.
> (d) What number of counts would you use on the assumption that 10
> packages are processed each year?
看不懂...
> (e) What is your probability of detecting a radioactive package if=1/8?
甚麼東西 "=1/8"?
> 我很努力的想 也只可能知道第一提可能的解答是什麼
> 我會再努力看看 也希望板上的大家可以給我一點指引..
> 真的很感謝你們^^
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