

\subsection{\bf Interpretation of Bayes Formulation}
\subsection{\bf of Likelihood---I}

\begin{slide}
\begin{itemize}
\item Consider Equation~(14)

\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 ($\alpha$ ) We can ignore $P\left( x_i \vert T \right)$ because
it is independent of $\alpha$ and fixed for our given $x_i$ and $T$.

\begin{description}
\item{$\bullet$} This has the practical consequence that the likelihood
is never normalized sensibly.
\end{description}

\item ($\beta$ ) $P\left( \alpha \vert T \right)$ philosophically
represents a priori knowledge of $\alpha$ before experiment
(measurement of $x_i$) performed.  

\begin{description}
\item{$\bullet$} This is shaky---not just because we don't really know 
how to define what $\vert T$ (``given $T$'') means
\item{$\bullet$} but, for instance, suppose we wish to parameterize
the simplest idea---``complete ignorance'' of $\alpha$ before experiment 
performed.
\end{description}
\end{itemize}
\end{slide}

