deletions | additions       diff --git a/However_as_the_frequency_of__.tex b/However_as_the_frequency_of__.tex  index 65a7a3b..ee3feda 100644  --- a/However_as_the_frequency_of__.tex  +++ b/However_as_the_frequency_of__.tex 
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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)}  \end{equation}  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 smoothing,  adding α =0.1 to the frequency count, \cite{wiki:additivesmoothing}. The results are summarized in Table (1):