

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

\begin{slide}
\begin{itemize}
\item Natural parameterization of ignorance is $P(\alpha\vert T) = $ 
constant.  

\item But suppose we put $\beta = \alpha^2$ and then $\beta$ has a
priori probability $\phi (\beta/T)$
\begin{eqnarray*}
\phi (\beta \vert T) d\beta & = & P(\alpha \vert T ) d\alpha ,
\hspace{1em} \mbox{i.e.,} \\
\phi (\beta \vert T) & = & \frac{1}{2\sqrt{\beta}} \neq \mbox{constant}
\end{eqnarray*}

\item So the concept of ``complete ignorance'' is not well defined, as
change of variables changes concept.

\begin{description}
\item{$\bullet$} Jeffreys (a big bad English-Oxford University Press
book cited in Mathews and Walker) spends 100's of pages trying to avoid
this difficulty.
\item{$\bullet$} His efforts are, in my opinion, so much garbage.
\end{description}

\item Fortunately, there is no trouble for large $n$ because of both an
obvious numerical reason (see next slide (The Likelihood Maximizes) and
a not so obvious mathematical reason (see slide (General Maximum
Likelihood Methods)).
\end{itemize}
\end{slide}

