

\begin{slide}
\subsection{\bf The Bayes Controversy}
\subsection{\bf Naive Application for Estimation---III}
\begin{itemize}
\item Problems with this application of Bayes Theorem are that:

\item a) $\alpha$ is not a random variable---it only takes one value.
Answer: Our knowledge of $\alpha$ can be considered as a random variable.

\item b) What is $P(B)$?  We will discuss this so called a priori knowledge
of $B$ later on---it essentially summarizes all previous (other) knowledge of
$\alpha$ gained from previous (other) experiments.

\item c) What is $P(A)$?  The probability of measurement of $\theta$
given any possible $\alpha$.  

\begin{description}
\item{$\bullet$} Nobody knows what this is!  
\item{$\bullet$} You essentially determine it by normalizing $P(B/A)$
or equivalently note that relative probabilities
\[
\frac{P\left(B_1/A\right)}{P\left(B_2/A\right)} = \frac{P\left(A/B_1\right)
P\left(B_1\right)}{P\left(A/B_2\right) P\left(B_2\right)}
\]
are indeed independent of the noxious $P(A)$.
\end{description}
\end{itemize}
\end{slide}

