}
\end{center}
\end{figure}
For this example, the MES given by equation (\ref{MES}) is $19.1$ whereas the sum over all the $z_j$ is $27.76$.  The $z_j$ components and $q_j$ components, given by summing over the points in the corresponding plots, are:
\begin{eqnarray}
\nonumber
&z_1 = 9.33, \ \  q_1 = 0.334&  \\
\nonumber
&z_2 = 9.03, \ \  q_2 = 0.332&  \\
\nonumber
&z_3 = 9.32, \ \  q_3 = 0.333&  \\
&Z = z_1 + z_2 + z_3 = 27.76 \ \.
\end{eqnarray}
Note that these values have been rounded.  The $\chi^2$ can then be computed:
\begin{equation}
\chi^2_{(2)} = \sum_{j=1}^3 (z_j - q_jZ)^2/q_j = 0.124 \ \,
\end{equation}
with an associated probability computed by equation (\ref{cumProb}):
\begin{equation}
P_{\chi^2 \geq 0.124} = 1 - P_{\chi^2<0.124} = 94\% \ \,
\end{equation}
and $\eta$ given by:
\begin{equation}
\eta = MES/\chi_r = 76.6 \ \.
\end{equation}
So this is a very simple detection as it should be, but it serves to illustrate how the calculation works.

Now, the same three square waves will be injected except that the last one will have its duration halved by a factor of two. The results obtained are now:
\begin{eqnarray}
\nonumber
&z_1 = 9.22,  \ \ q_1 = 0.334& \\
\nonumber
&z_2 = 8.89,  \ \ q_2 = 0.332& \\
\nonumber
&z_3 = 4.43,  \ \ q_3 = 0.333& \\
&Z = z_1 + z_2 + z_3 = 22.54 \ \.
\end{eqnarray}
The MES is then $17.05$ and the $\chi^2$, probability, and $\eta$ can then be computed:
\begin{equation}
\chi^2_{(2)} = \sum_{j=1}^3 (z_j - q_jZ)^2/q_j = 42.89 \ \,
\end{equation}
\begin{equation}
P_{\chi^2 \geq 42.89} = 1 - P_{\chi^2<42.89} = 4.8\times10^{-8}\% \ \,
\end{equation}
\begin{equation}
\eta = MES/\chi_r = 3.68 \ \.
\end{equation}
This illustrates how sensitive the veto is to mismatch in signal and template.

As another example, the same three square waves will be injected except the last one will now have its amplitude reduced by a factor of two.  The results obtained are now:
\begin{eqnarray}
\nonumber
&z_1 = 8.80,  \ \ q_1 = 0.335&  \\
\nonumber
&z_2 = 8.50,  \ \ q_2 = 0.332&  \\
\nonumber
&z_3 = 4.30,  \ \ q_3 = 0.334&  \\
&Z = z_1 + z_2 + z_3 = 21.60 \ \.
\end{eqnarray}
The MES is then $16.28$ and the $\chi^2$, probability, and $\eta$ can then be computed:
\begin{equation}
\chi^2_{(2)} = \sum_{j=1}^3 (z_j - q_jZ)^2/q_j = 38.20 \ \,
\end{equation}
\begin{equation}
P_{\chi^2 \geq 38.20} = 1 - P_{\chi^2<38.20} = 5.07\times10^{-7}\% \ \,
\end{equation}
\begin{equation}
\eta = MES/\chi_r = 3.73 \ \.
\end{equation}
So the veto is sensitive to a mismatch in depth of one of the pulses as well.  

A logical extension of this would be to ask: how do these numbers change when there are more transits and still only a single transit is perturbed in some way?  When the degrees of freedom get large enough, the effect will get washed out to the point that the veto will no longer work.  This behavior is acceptable in this case however, because if there are say, $10$ transits, and only one of them is perturbed in some way, we would still have reasonable belief there is something interesting in the data.  Clearly though, if many of the transits do not match well then the veto will work as it should.    

\section{Results}
\label{s:results}
As described in \cite{Tenenbaum:2012ft}, events that pass the MES threshold of $7.1$ in TPS are then subjected to both a robust statistic test as well as the two $\chi^2$ tests mentioned in section~\ref{s:thresholds}, in that order.  Recently, TPS was run over a set of $192,312$ targets, (known eclipsing binaries were all removed), with quarters $Q1-Q12$, and with the $\chi^2$ thresholds turned down to gain an understanding of their operating characteristics.  The set of Kepler Objects of Interest (KOI's) was used to understand the detection probability.  The set of KOI's is comprised mostly of known planets as well as planet candidates which have not gone through the vetting process.  A set of $2,211$ KOI stars, the best of the best, were set aside to examine the detection probability.  To understand the false alarm probability, the full set of $3009$ unique KOI target stars were removed from the total set of targets, the remainder of which forms the false alarm population of targets.  Of course, some of these false alarms may actually be true positives, but it is thought that the number is fairly low.  It should also be noted that the false alarm and detection probabilities gleaned by a study of this sort are only to be used as an indicator since the true pipeline version of TPS allows for searching over many period and epoch combinations, for each target, that produce a MES above threshold.  Here we have limited the number of searched combinations to only one per target.  

After applying the MES threshold of $7.1$, there are $14$ targets that get filtered out of the $2,211$ KOI's, giving a $99.4\%$ detection probability.  There are then $86,737$ non-KOI targets that produce ``false alarms'', for a false alarm rate of $45.8\%$.  Applying the robust statistic threshold of $\eta = 6.4$ filters out an additional $13$ of the $2,211$ KOI's for an overall detection probability of $98.8\%$.  The number of non-KOI targets producing false alarms is reduced to $40,880$, for an overall false alarm rate of $21.6\%$.  Now we will just use these two sets of remaining targets namely, the set of $2,184$ KOI's and the set of $40,880$ non-KOI's, to explore various thresholds on $\eta_{(m)}=MES/\chi_{(m)r}$.  Figure \ref{f:OC} shows the operating characteristic curve for each $\eta$ individually.  You can clearly see that $\eta_{(2)}$ achieves the best detection efficiency but would still, for some reasonable detection probability, let through an unacceptable number of false alarms if used alone. In figure \ref{f:probs}, the corresponding false alarm and detection probabilities are plotted as a function of threshold $\eta_{\ast}$.  

\begin{figure}
\begin{center}
\epsfig{file=Fig2_OC,width=3.4in}
\caption{ \label{f:OC} Operating characteristic curve for the three vetoes of interest.  }
\end{center}
\end{figure}

\begin{figure}
\begin{center}
\epsfig{file=Fig3_Probs,width=3.4in}
\caption{ \label{f:probs} False alarm and detection probabilities corresponding to the operating characteristic curves in figure \ref{f:OC}.  }
\end{center}
\end{figure}

As mentioned in \cite{Tenenbaum:2012ft}, TPS currently uses $\eta_{(1)}$ and $\eta_{(2)}$ for vetoing purposes, the threshold for both set to $7.0$.  Using $\eta_{(3)}$ instead of $\eta_{(1)}$ is the subject of ongoing work but is desirable due