However, as the frequency of the joined event of numerous features \((X_{1..n})\) is usually zero or close to zero, and thus inappropriate to estimate a probability, there is an expanded form of this equation that allows to estimate the probability on the basis of the independent events\cite{wiki:bayes}.

然而，由於這些條件 \((X_{1..n})\)經常為0或趨近於0(因為存留至今的明墓為數稀少)，使得計算機率的算式可能皆是0或無意義。於是考慮到這些狀況的情況下，本團隊將利用了此算式的擴展式，得以單算獨立事件的機率\cite{wiki:bayes}。算式如下。

\[P(明代|X_{1..n}) = \frac{P(明代) * \prod\limits_{i=1}^{n} P(X_{i}|明代) }{P(明代) * \prod\limits_{i=1}^{n}P(X_{i}|明代) + P(非明代) * \prod\limits_{i=1}^{n} P(X_{i}|非明代)}\]

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):

因此，我們利用分布在台澎金馬的墓碑來做為計算此墓為明墓的條件，首先先單獨計算，然後再使用延伸的算式合併。對於所有的估算，本團隊利用控制理論（拉普拉斯平滑處裡\cite{wiki:additivesmoothing}）來避免零概率的問題，結果簡介於下圖。