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Tommaso Treu edited Challenge Structure.tex
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\subsubsection{TDC0}
Every prospective good team is invited to download the $N$ TDC0 pairs of light curves and analyze them. Upon completion of the analysis, the time delays estimates together with the estimated 68\% uncertainties will be uploaded to a designated web site. The simulation team will calculate four standard metrics given a set of estimated time delays $\tilde{\Delta t}$ and uncertainties
$\delta \tilde{\Delta t}$. $\sigma$. The first one is robustness, quantified as the fraction of light curves $f$ for which an estimate is obtained. The second one is the goodness of fit of the estimates, quantified by the standard $\chi^2$
\begin{equation}
\chi^2=\sum_i \left(\frac{\tilde{\Delta t}_i - \Delta
t_i}{\delta \tilde{\Delta t}_i}\right)^2 t_i}{\sigma_i}\right)^2
\end{equation}
The third metric is the precision of the estimator, quantified by the average relative uncertainties
\begin{equation}
P=\frac{1}{fN}\sum_i
\left(\frac{\delta\tilde{\Delta_t}}{\Delta t}\right) \left(\frac{\delta\tilde{\Deltat}_i}{\Delta t_i}\right)
\end{equation}
The fourth is the accuracy of the estimator, quantified by the average fractional residuals
\begin{equation}
A=\frac{1}{fN}\left|\sum_i \left(\frac{\tilde{\Delta t}_i - \Delta t_i}{\Delta
t}\right)\right| t_i}\right)\right|
\end{equation}
The initial function of these metrics is to define a minimal performance threshold that must be passed, in order to guarantee meaningful results in TDC1. To pass TDC0, an analysis team's results must satisfy the following criteria.