

\subsection{\bf Correlated Observations in $\chi^2$}

\begin{slide}
\begin{itemize}
\item Note that if $x_i$ are calculated from the same population,
e.g.,
\begin{eqnarray*}
x_1 & = & \frac{1}{n} \sum^m_{k=1} y_k \\
&& \\
x_2 & = & \frac{1}{n} \sum^m_{k=1} y^2_k ,\ \ \ \mbox{etc.}
\end{eqnarray*}

\item Then they are not independent, 

\item but we can use the theorem proved at the end of Section~2 to show
that $x_i$ will (for large $m$) be Gaussian.

\item However, there is a correlation matrix, i.e., $L\propto\exp
\left\lbrace - \frac{1}{2} ({\rm x} - \xi)^T M({\rm x} - \xi)
\right\rbrace$ as discussed in Solmitz.

\item By diagonalizing $M$ we can (in principle) reduce this to the
usual $\chi^2$ method with $x_i$ replaced by eigenvectors of $M$.
\end{itemize}
\end{slide}

