## Appendix B Choice of \((\rho,\lambda,\rho)\) Based on a Case Study
\begin{table}
\begin{tabular}{l l c c c c c c c c c c c c c c c c} \hline  & & \multicolumn{3}{c}{**Step 1-3**} & \multicolumn{3}{c}{**Step 4-5**} & \multicolumn{3}{c}{**\(\mathcal{L}^{\mathrm{max}}\)**} & \multicolumn{3}{c}{**\(\mathcal{L}^{\mathrm{max}}\)**} & \multicolumn{3}{c}{**\(\mathcal{L}^{\mathrm{max}}\)**} & \multicolumn{3}{c}{**\(\mathcal{L}^{\mathrm{max}}\)**} & \multicolumn{3}{c}{**\(\mathcal{L}_{\mathrm{max}}\)**} \\ \cline{2-13} \(\rho_{\lambda}\),\(\rho_{\lambda}\) & & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) & \(\tau_{\lambda}\) \\ \hline \multirow{2}{*}{LLN} & Avg & 0.548 & 0.504 & 0.655 & 0.94 & 0.99 & 0.03 & 0.02 & 0.02 & 1.77 & \(9.95\times 10^{-4}\) & \(4.5\times 10^{-5}\) & \(5.3\times 10^{-5}\) & 46.6 & 46.2 & 125 & 0.003 \\  & Ma & 0.244 & 0.273 & 0.80 & 0.88 & 0.00 & 0.01 & 0.01 & 0.03 & 0.25 & \(4.7\times 10^{-5}\) & \(7.0\times 10^{-5}\) & \(5.4\times 10^{-5}\) & 21 & 22 & 18 & 0.007 \\  & Ma & 0.534 & 0.543 & 0.94 & 0.97 & 1.00 & 0.04 & 0.04 & 0.11 & 1.35 & \(1.4\times 10^{-5}\) & \(7.2\times 10^{-5}\) & \(2.0\times 10^{-5}\) & 77 & 74 & 280 & 0.116 \\ \cline{2-13}  & Avg & 0.548 & 0.465 & 0.955 & 0.95 & 0.85 & 0.83 & 0.03 & 0.02 & 0.03 & 0.88 & \(9.1\times 10^{-5}\) & \(4.5\times 10^{-5}\) & \(7.9\times 10^{-5}\) & 46.6 & 46.2 & 196 & 0.489 \\ LLN & Min & 0.294 & 0.073 & 0.930 & 0.88 & 0.35 & 0.01 & 0.01 & 0.02 & \(4.7\times 10^{-5}\) & \(7.0\times 10^{-5}\) & \(7.2\times 10^{-5}\) & 21 & 12 & 12 & 0.296 \\  & Ma & 0.534 & 0.999 & 0.974 & 0.97 & 0.97 & 0.97 & 0.94 & 0.04 & 0.12 & \(3.86\times 10^{-5}\) & \(6.7\times 10^{-5}\) & \(7.3\times 10^{-5}\) & 77 & 74 & 255 & 0.584 \\  & Ma & 0.538 & 0.290 & 0.955 & 0.95 & 0.95 & 0.93 & 0.03 & 0.03 & 1.96 & \(9.9\times 10^{-5}\) & \(7.2\times 10^{-5}\) & \(7.2\times 10^{-5}\) & 21 & 21 & 113 & 0.200 \\  & Ma & 0.294 & 0.080 & 0.910 & 0.89 & 0.35 & 0.01 & 0.01 & 0.00 & 0.25 & \(4.7\times 10^{-5}\) & \(7.2\times 10^{-5}\) & 21 & 21 & 131 & 0.200 \\  & Ma & 0.534 & 0.862 & 0.504 & 0.97 & 0.97 & 0.94 & 0.04 & 0.04 & 0.12 & \(4.22\times 10^{-5}\) & \(1.0\times 10^{-5}\) & \(1.2\times 10^{-5}\) & 23 & 27 & 285 & 0.551 \\ \hline \multirow{2}{*}{NLL} & Avg & 0.548 & 0.423 & 0.565 & 0.95 & 0.99 & 0.03 & 0.02 & 0.03 & 1.25 & \(1.0\times 10^{-4}\) & \(4.6\times 10^{-5}\) & \(7.3\times 10^{-5}\) & 46.8 & 46.7 & 196 & 0.428 \\  & Ma & 0.389 & 0.995 & 0.95 & 0.92 & 0.03 & 0.01 & 0.01 & 0.03 & 0.25 & \(3.5\times 10^{-5}\) & \(7.6\times 10^{-5}\) & 25 & 29 & 0.329 & 0.329 \\  & Ma & 0.535 & 0.997 & 0.974 & 0.97 & 1.00 & 0.04 & 0.04 & 0.13 & \(4.5\times 10^{-5}\) & \(7.5\times 10^{-5}\) & \(7.2\times 10^{-5}\) & 74 & 66 & 300 & 0.535 \\  & Ma & 0.538 & 0.550 & 0.955 & 0.95 & 0.85 & 0.03 & 0.03 & 0.03 & 1.36 & \(9.9\times 10^{-5}\) & \(9.9\times 10^{-5}\) & \(6.9\times 10^{-5}\) & 26 & 46 & 46.6 & 225 & 0.352 \\  & Ma & 0.294 & 0.076 & 0.910 & 0.89 & 0.35 & 0.01 & 0.01 & 0.00 & 0.25 & \(4.7\times 10^{-5}\) & \(7.2\times 10^{-5}\) & 23 & 21 & 21 & 113 & 0.294 \\  & Ma & 0.584 & 0.999 & 0.974 & 0.97 & 0.97 & 0.94 & 0.04 & 0.12 & 4.22 & \(1.6\times 10^{-5}\) & \(1.0\times 10^{-5}\) & \(7.3\times 10^{-5}\) & 77 & 27 & 258 & 0.584 \\ \cline{2-13}  & Avg & 0.588 & 0.446 & 0.955 & 0.95 & 0.99 & 0.03 & 0.03 & 0.02 & 1.25 & \(1.0\times 10^{-5}\) & \(6.9\times 10^{-5}\) & \(2.3\times 10^{-5}\) & 46.8 & 46.7 & 196 & 0.438 \\  & Ma & 0.530 & 0.550 & 0.94 & 0.97 & 0.97 & 0.94 & 0.04 & 0.04 & 0.13 & \(4.5\times 10^{-5}\) & \(1.5\times 10^{-5}\) & \(2.7\times 10^{-5}\) & 25 & 25 & 56 & 0.002 \\ \hline \multirow{2}{*}{NNL} & Avg & 0.588 & 0.531 & 0.565 & 0.95 & 0.96 & 0.96 & 0.03 & 0.03 & 1.39 & \(1.0\times 10^{-5}\) & \(5.0\times 10^{-5}\) & \(6.9\times 10^{-5}\) & 46.8 & 46.8 & 224 & 0.552 \\  & Ma & 0.350 & 0.567 & 0.95 & 0.95 & 0.97 & 0.92 &Table 14 summarizes the main findings from the comparison study for different interpolation techniques.