\begin{table}%T3
\caption{\label{tab:popsims_results}Unmarginalized, best-fit parameters for mock data sets.}
\small%\centerline
{
\begin{tabular}{llll}
\hline\hline
\multicolumn{1}{c}{Parameter} &
\multicolumn{1}{c}{Input value} &
\multicolumn{2}{c}{Best-fit with 68\% errors}\\
\multicolumn{1}{c}{}&
\multicolumn{1}{c}{}&
\multicolumn{1}{c}{Idealized} &
\multicolumn{1}{c}{115 $h^{-1}$ Mpc box } \\
\hline 
faint: & & &\\
~~~~~~~~~~log($M_{1}$) & 12.826 & $\rm 12.836^{+0.032}_{-0.042}$ & $\rm 12.673^{+0.195}_{-0.149}$ \\
\noalign{\smallskip}
~~~~~~~~~~$\alpha$      & 0.9    & $\rm 0.900^{+0.020}_{-0.024}$ & $\rm 0.853^{+0.124}_{-0.094}$\\
\noalign{\smallskip}
~~~~~~~~~~log($M_{\rm cut}$) & 11.544 & $\rm 11.561^{+0.057}_{-0.082}$ & $\rm 11.691^{+0.316}_{-0.378}$\\
\noalign{\smallskip}
\hline
%&&&\\
bright: & &&\\
~~~~~~~~~~log($M_{1}$) & 13.301 & $\rm 13.341^{+0.041}_{-0.079}$ & $\rm 13.304^{+0.131}_{-0.275}$ \\
\noalign{\smallskip}
~~~~~~~~~~$\alpha$      & 1.0    & $\rm 1.042^{+0.041}_{-0.071}$ & $\rm 1.055^{+0.122}_{-0.238}$\\
\noalign{\smallskip}
~~~~~~~~~~log($M_{\rm cut}$)& 12.301 & $\rm 12.157^{+0.223}_{-0.218} $ & $\rm 10.888^{+1.654}_{-1.888}$\\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
$f$                & 1.0    & $\rm 1.017^{+0.119}_{-0.159} $ & $\rm 0.890^{+0.809}_{-0.446}$\\
\noalign{\smallskip}
$f_{\rm cross}$    & 1.0    & $\rm 0.981^{+0.150}_{-0.122}$ & $\rm 1.051^{+1.087}_{-0.488}$\\
\hline 
\end{tabular}}
\smallskip
 Note: masses are in $h^{-1}~M_{\odot}$.
\end{table}