Estimating the Probability of a Ming Tombstone

在考古學範疇中,使用條件機率計算其可能性是相當常見地\cite{Barcelo09a}:在某特定條件下(\(X_{1..n}\)),此情況(此墓卑為明代之墓)發生的機率為何。見算式1。除了此公式外,有另外一個延伸的公式允許我們算出特定獨立事件,我們利用此公式計算在台澎金馬的明墓中,此「洪媽楊氏墓」碑為明墓的機率為合,並在與第一個算式的結果作計算討論。 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, given the tomb features \(X_{1..n}\) is written as. 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.We thus calculate the probability of a Ming tombstone conditioned by some of the tomb attributes discussed above for Taiwan, Penghu and Jinmen, first in isolation and then combining them through the formula (2).

For all estimates we use additive smoothing, which is also called Laplace (拉普拉斯) smoothing, adding α =0.1 to the frequency count, \cite{wiki:additivesmoothing}. The results are summarized in Table (1):

然而由於明代之墓所保存的樣本數量相當稀少,數值皆可能為0或趨近於0,導致機率算出來為0或無意義,因此採用拉普拉斯平滑處理法\cite{wiki:additivesmoothing},使得計算上較便利。