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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}
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 $X_{1}$, $X_{2}$ and $X_{3}$ is written
as P(
mated as in. as.
\begin{equation}
P(明代|X_{1..n}) = \frac{P(X_{1..n}|明代) * P(明代)}{P(X_{1..n})}
\end{equation}
However, as the frequency of the joined event of numerous features $(X_{1..n})$ is usually zero or close to zero, and thus not appropriate to estimate the probability, there is an expanded form of this equation that allows to estimate the probability on the basis of the independent
events. events\cite{wiki:bayes}.
\begin{equation}
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)}