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Oliver Streiter edited section_Estimating_the_Probability_of__.tex
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\section{Estimating the Probability of a Ming Tombstone}
檢測此碑為明墓的可能性
It is common practice in archeology to calculate conditional probabilities of invisible properties of an artifact or a site given the know frequency distributions of visible properties of the same artifact of site in relation to a larger sample of know cases \cite{Barcelo09a}. The conditional property (P) of being a Ming tombstone (M), given the tomb features $X_{1}$, $X_{2}$ and $X_{3}$ is written as P(M|ABC) and be estimated as in.
再考古學的範疇內利用條件機率來計算某物品的潛在機率是相當常見的。在某一特定條件(X_{1..n})下,此墓為明墓的機率為(M)。判斷此墓的指標由X1,X2,X3表示,此算式寫做P(M|ABC) 。
\begin{equation}
P(M|X_{1..n}) = \frac{P(X_{1..n}|M) * P(M)}{P(X_{1..n})}
\end{equation}
However, as the probability of the joined event of numerous features
(X_{1..n}) $(X_{1..n})$ is usually zero or close to zero, there is an expanded form of this equation that allows to estimate the joined events from the independent events where $-M$ represents all but Ming period tombstones.
然而,在此某特定條件下因為樣本數過少,時常為0或趨近於0,於是利用一個擴大範圍的算式使得其他的墓也能被計算,只有明墓作為一個獨立事件。
\begin{equation}
P(M|X_{1..n}) = \frac{P(M) * \prod\limits_{i=1}^{n} P(X_{i}|M) }{P(M) * \prod\limits_{i=1}^{n}P(X_{i}|M) + P(-M) * \prod\limits_{i=1}^{n} P(X_{i}|-M)}