

\subsection{\bf Enter Mr. Bayes}
\subsection{\bf for Conditional Probablities---II}

\begin{slide}
\begin{itemize}
\item Equation~(14) is the essence of the maximum likelihood principle.

\begin{displaymath}
P \left( \alpha \vert x_i , T \right) = P \left( x_i \vert \alpha , 
T \right) \frac{P (\alpha \vert T)}{P (x_i \vert T)}
\end{displaymath}

\item Equation~(14) converts the likelihood $L\left( x_1 \ldots x_n
\right) = P\left( x_i \vert \alpha , T \right)$

\begin{description}
\item{$\bullet$} which is a function or probability of $x_i$ for fixed
$\alpha , T$
\item{$\bullet$} into $P\left( \alpha \vert x_i , T \right)$ which is
the desired probability distribution of $\alpha$ for given measurements
$x_i$ and prejudices $T$.
\end{description}
\end{itemize}
\end{slide}

