

\subsection{\bf Individual Events Become}
\subsection{\bf Binned Data---II}

\begin{slide}
\begin{itemize}
\item However, even if $N$ is not so large that $p$ is constant in each
group, then one can still bin data and {\em throw away exact\/} values
of $x_i$ for each event---just record what bin it is in.

\item Obviously, if $p$ is not constant over each bin, this throws away
information.

\item However, Equation~(25) is now exact for $L$ and one chooses bins
so that $n_k$ is large and $\chi^2$ applicable.

\item This is used in practice because $\chi^2$ is so much easier and
cheaper to use.

\item Often one can bin data and minimize $\chi^2$: this gives values
for theoretical parameters which can be used as initial values for
expensive full likelihood fit which will then need only a few
iterations.

\item One can carry piggy back further---and use a super low grade
method (e.g., method of moments---see Section~3.5) to initialize
parameters before $\chi^2$ fit.

\item This is discussed by Solmitz (``histogram method'') and Eadie,
et al.
\end{itemize}
\end{slide}

