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zdOS{=#|Qf)@tr+-iQ4uA%%PTxK8;?fie1LF7lmzXJ<4XgeLjescF_EYD`NJZeG#=C zNUEDsEzDWhO>R3LUH=Rm7VzP7$`LS{yxw&Vd)Y*;2~%S0XieJL&<}eOX7{fet!2&F zk&_Fn;bvoGw$Kht-] (T1.south) -- (DepRes.north); + \draw[->] (T2.south) -- (DepRes.north); + \draw[->] (bio.south) -- (T1.north); + \draw[->] (bio.south) -- (T2.north); + \end{tikzpicture} +\end{center} + +\vskip 5pt +\begin{center} + \vskip 5pt + \begin{tabular}{| c | c | c |} + \hline + Test 1 Result & Test 2 Result & P(A) \\ + \hline\hline + \multicolumn{3}{| c |}{Prior beliefs of test 1} \\ + \hline + Unknown & Unknown & 10\% \\ + Positive & Unknown & 67.857\% \\ + Negative & Unknown & 0.581\% \\ + \hline + \multicolumn{3}{| c |}{Prior beliefs of test 2} \\ + \hline + Unknown & Positive & 55\% \\ + Unknown & Negative & 1\% \\ + \hline + \multicolumn{3}{| c |}{Dependent results from both tests} \\ + \hline + Positive & Positive & 75\% \\ + Positive & Negative & 1.5\% \\ + Negative & Positive & 0.6\% \\ + Negative & Negative & 0.087\% \\ + \hline + \end{tabular} +\end{center} +Note that this probability of positive results in both tests (which both have greater than 50\% of positives being true positives) is as certain as two positives +from two completely independent tests with 50\% of positives being true. If the partial dependence was not included in the calculation, as would have occured in a +Naive Bayes model, the model's listed accuracy would be inflated. + +\newpage +\section{Unit 4: Markov Chains} \end{document} \ No newline at end of file