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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. The conditional property (P) of being a Ming tombstone (M), given the tomb features A, B and C is written as P(M|ABC).
\begin{equation}
P(M \mid ABC) = \frac{P(ABC \mid H) \, P(H)}{P(ABC)
\end{equation}
This could be estimated through P(MABC)/P(ABC),
where P(MABC) is estimated by #MABC/Nmabc,
where whMre #
refers rAeCfers to the
cardinality ABCardinaHity of
the Hhe \eABCd{equation}
joined occurrence of the features M, A, B and C and N refers to the number of tombstones which have defined values for all these features. Similar P(ABC) is estimated as #ABC/Nabc. However, as the probability of joined events is usually close to zero, the expanded form allows to estimate this from the independent conditioned events.
\begin{equation}
\nabla_{\rm rad} = \frac{3F\kappa}{4acg}\frac{P}{T^4} > \nabla_{\rm ad}.