## 4 Empirical Study
### Results with LGPIF (H = 1679)
\begin{table}
\begin{tabular}{c c|c c c|c} \hline \hline \(\zeta=0.6\) & \multirow{2}{*}{**Feature**} & **Model (A)** & **Model (B)** & **Model (C)** & **Model (D)** \\ \(R_{e_{x}}=0.10\) & & **Gold** & **with** & **Gustafson** & **SIMEX** \\ \cline{2-6}  & & **Standard** & **Model Risk** & **Correction** & **Correlation** \\ \hline \multirow{3}{*}{\(f(ln\tilde{Y}_{h}|\mathbf{X}^{S})\)} & LPPD & \(-16\),155.90 & \(-17\),731.03 & \(-16\),390.44 & - \\ \cline{2-6}  & SSPE & 784.52 & 840.02 & 795.07 & 892.72 \\ \cline{2-6}  & SAPE & 415.21 & 430.22 & 418.68 & 439.92 \\ \cline{2-6}  & \(D_{KL}\) & 0.00 & 1.57 & 0.41 & - \\ \hline \multirow{3}{*}{\(f(lnS_{h}|\mathbf{X}^{F},\mathbf{X}^{S})\)} & CTE 10\% & 48,782.40 & 50,222.22 & 49,764.81 & 45,846.51 \\ \cline{2-6}  & CTE 50\% & 81,593.58 & 84,118.93 & 83,595.88 & 73,558.45 \\ \cline{1-1} \cline{2-6}  & CTE 90\% & 209,761.38 & 233,257.58 & 221,359.16 & 129,851.81 \\ \cline{1-1} \cline{2-6}  & CTE 95\% & 274,996.31 & 295,325.47 & 281,371.20 & 164,324.93 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of predictive performances among three Bayesian hierarchical GLMs—Model (A), -(B), and -(C)—and the GLM-based SIMEX, based on the LGPIF data with a covariate error rate of \(R_{e_{x}}\)= 0.10 and a scaling factor of \(\zeta=0.6\). \begin{table}
\begin{tabular}{c c|c c c|c} \hline \hline \(\zeta=0.5\) & \multirow{2}{*}{**Feature**} & **Model (A)** & **Model (B)** & **Model (C)** & **Model (D)** \\ \(R_{e_{x}}=0.40\) & & **Gold** & **with** & **Gustafson** & **SIMEX** \\  & & **Standard** & **Model Risk** & **Correction** & **Correlation** \\ \hline \multirow{3}{*}{\(f(ln\tilde{Y}_{h}|\mathbf{X}^{S})\)} & LPPD & \(-16\),155.90 & \(-17\),437.59 & \(-16\),770.85 & - \\ \cline{2-6}  & SSPE & 784.52 & 817.16 & 798.89 & 816.80 \\ \cline{2-6}  & SAPE & 415.21 & 422.53 & 419.83 & 421.60 \\ \cline{2-6}  & \(D_{KL}\) & 0.00 & 1.28 & 0.61 & - \\ \hline \multirow{3}{*}{\(f(ln\tilde{Y}_{h}|\mathbf{X}^{S})\)} & CTE 10\% & 48,782.40 & 42,995.64 & 49,599.75 & 45,237.36 \\ \cline{2-6}  & CTE 50\% & 81,593.58 & 89,103.11 & 82,218.10 & 78,736.26 \\ \cline{1-1} \cline{2-6}  & CTE 90\% & 209,761.38 & 226,599.19 & 196,273.16 & 121,342.20 \\ \cline{1-1} \cline{2-6}  & CTE 95\% & 274,996.31 & 260,859.33 & 269,656.52 & 170,487.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of predictive performances among three Bayesian hierarchical GLMs—Model (A), -(B), and -(C)—and the GLM-based SIMEX, based on the LGPIF data with a covariate error rate of \(R_{e_{x}}\)= 0.01 and a scaling factor of \(\zeta=0.6\). Figure 6: Curve alignment under the condition of ‘error rate \(R_{e_{x}}=0.01\)’ with \(\zeta=0.6\): cluster-wise histograms (for \(j=1,\ldots 6\)) of the observed claim amount \(Y_{h}\) on a log scale and the out-of-sample predictive densities obtained from Model (A), -(B), and -(C). Figure 8: _Cont_. Figure 7: Curve alignment under the condition of ‘error rate \(R_{e_{s}}=0.10\)’ with \(\zeta=0.6\): cluster-wise histograms (for \(j=1,\ldots 6\)) of the observed claim amount \(Y_{h}\) on a log scale and the out-of-sample predictive densities obtained from Model (A), -(B), and -(C).