

\subsection{\bf What I Used to Do!}

\begin{slide}
\begin{itemize}
\item In a program that I used for many years successfully, I chose
$L$ by the largest value such that
\[
\lambda_L \ge r\lambda_1 \ \ \mbox{and} \ \ \lambda_{L+1} < r\lambda_1
\]

\item where initially the ratio $r=0.1$ and $r$ was increased or
decreased based on experience,

\item i.e., if the resultant $\chi^2 \left( \Underline{$\beta$}_0 +
\Delta\beta \right)$ was indeed smaller (as predicted) or larger than
$\chi^2 \left(\Underline{$\beta$}_0 \right)$.

\item This method is equivalent to replacing $M$ by the regularized
version.

\vspace*{10pt}
\centerline{\psfig{figure=fig19.phys.ps,clip=true,width=4.0in}}
\vspace*{10pt}
\end{itemize}
\end{slide}

