

\begin{slide}
\subsection{\bf The Bayes Controversy}
\subsection{\bf Naive Application for Estimation---I}
\begin{itemize}
\item Now we have derived Bayes theorem where $A$ and $B$ are (Borel) sets
in a space populated by a random variable.  

\item Now a useful ``application'' of theorem is take the following
choice of sets:

\begin{description}
\item{A:} to be Borel set given a set of experimental results---this is
correct.
\item{B:} to be a set of hypotheses, e.g., a set in space of values of a
theoretical parameter---this will turn out to be flaky.
\end{description}
\end{itemize}

Consider an example:
\begin{itemize}
\item We measure scattering angles $\theta$ and wish to find $\alpha$

\item when probability of observing

$\theta$ is $P(\theta ) = \frac{1}{2(1 + \alpha\cos\theta )}$.
\begin{description}
\item{$\bullet$} Here, $A$ is a set in $\theta$ space.

\item{$\bullet$} $B$ is a set in $\alpha$ space.
\end{description}
\end{itemize}
\end{slide}

