

\subsection{\bf Estimate of Errors to be Used}
\subsection{\bf in $\chi^2$ Fits}

\begin{slide}
\begin{itemize}
\item One should also mention that there are two versions of $\chi^2$
depending on whether error $\sigma_i$ taken from ``experiment'' or
``estimated theoretically.''

\item In the latter case, it will be a function of the parameters to be
varied.

\item For example, suppose $x_i$ is number of events in some counting
experiment.  

\begin{description}
\item{$\bullet$} The $\sigma_i$ (experimental) $ = \sqrt{x_i}$ 
\item{$\bullet$} but $\sigma_i$ (theory) $= \sqrt{\xi_i}$.  
\end{description}

\item Now $x_i$ is only Gaussian for large $x_i$, but then $\sqrt{x_i}$
and $\sqrt{\xi_i}$ are essentially same.

\item If $x_i = 0$, then theoretical $\sigma$ is to be
preferred!---although $\chi^2$ method itself is in difficulties as
$x_i$ not Gaussian.

\item It is technically best to go back to maximum likelihood and put
in true Poisson distribution for $x_i$.
\end{itemize}
\end{slide}

