\begin{table}%T1
%\centering
\par
\caption{Results of numerical experiments comparing age determination
methods using the step method, the corrected step method, the Monte~Carlo
method, and Bayesian estimation. Each line gives summary statistics from
1000 independent sets of synthetic data generated with the uncertainties
specified in the first three columns. All ages are in Gyr.
See Sect.~\ref{sec:numex} for further explanation.}
\label{tab2}
\begin{tabular}{@{\hspace*{-1.8cm}}c@{\hspace*{-2cm}}ccccccccc}
\hline\hline
\noalign{\smallskip}
\multicolumn{3}{c}{Assumed $\sigma$ in} &&
\multicolumn{6}{c}{Median $\tau_{\rm est}$, $\pm$median $\sigma_\tau$,~~%
(\% within CI),~~[median absolute deviation]} \\[-5pt]
\multicolumn{3}{c}{\hrulefill} &&
\multicolumn{6}{c}{\hrulefill} \\[1pt]
[Me/H] & $\log T_{\rm eff}$ & $M_V$
&& Step method & Corrected && Monte Carlo && Bayesian \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\hspace*{2cm}{Case 1: True age $\tau_{\rm true}=2.18$~Gyr}\\
\noalign{\smallskip}
0.05 & 0.005 & 0.05 && $2.19\pm 0.11$~(44\%)~[0.13] & $\pm0.19$~(67\%) &&
$2.16\pm 0.20$~(71\%)~[0.13] && $\rm 2.18^{+0.18}_{-0.20}$~(66\%)~[0.14] \\[3pt]
0.10 & 0.010 & 0.10 && $2.15\pm 0.24$~(42\%)~[0.27] & $\pm0.41$~(73\%) &&
$2.12\pm 0.51$~(75\%)~[0.32] && $\rm 2.20^{+0.36}_{-0.42}$~(68\%)~[0.25] \\[3pt]
0.20 & 0.020 & 0.20 && $2.05\pm 0.61$~(50\%)~[0.65] & $\pm1.05$~(77\%) &&
$2.13\pm 1.01$~(70\%)~[0.68] && $\rm 2.14^{+0.63}_{-0.88}$~(76\%)~[0.40] \\
\noalign{\bigskip}
\hspace*{2cm}{Case 2: True age $\tau_{\rm true}=2.85$~Gyr}\\
\noalign{\smallskip}
0.05 & 0.005 & 0.05 && $2.98\pm 0.13$~(48\%)~[0.23] & $\pm0.22$~(72\%) &&
$3.10\pm 0.49$~(68\%)~[0.27] && $\rm 2.83^{+0.21}_{-0.14}$~(72\%)~[0.09] \\[3pt]
0.10 & 0.010 & 0.10 && $3.13\pm 0.44$~(41\%)~[0.46] & $\pm0.76$~(64\%) &&
$3.17\pm 0.65$~(64\%)~[0.47] && $\rm 2.76^{+0.36}_{-0.27}$~(71\%)~[0.21] \\[3pt]
0.20 & 0.020 & 0.20 && $3.05\pm 0.66$~(44\%)~[0.69] & $\pm1.14$~(70\%) &&
$3.21\pm 1.10$~(69\%)~[0.70] && $\rm 2.60^{+0.61}_{-0.52}$~(70\%)~[0.37] \\
\hline
\end{tabular}
\end{table}