# Cognitive Artificial Intelligence Using Bayesian Computing Based on Hybrid Monte Carlo Algorithm
## 4 Experiments and Results
### Car Data Set  
We performed another experiment using the car data set provided by the R project [45]. This data set consisted of two variables, Speed and Dist. The data represent the stopping distance of cars according to their speed [35]. We considered the following model to present the performance and validity of our proposed method:  
\[Dist=\beta_{0}+\beta_{1}Speed+e \tag{14}\]  
In (14), the Dist and Speed are response and explanatory variables and \(e\) is the error term. This model has same structure of the model in (11). Table 5 presents the estimated parameters and HMC confidence intervals by confidence levels.  
Similar to the results presented in Table 3, as the significance level increases, the length of the HMC confidence interval increases. In the current paper, we used the significance level as the emotional degree. The result of the optimal and emotional decisions is presented in Table 6.  
From the results presented in Table 6, we can observe that the optimal values of GLM and HMC are similar to each other. When the emotional level of HMC is 0.5, all emotional values are similar to the optimal value of HMC; however, when the emotional level increases to 0.9, some values are far from the optimal value of HMC. Therefore, we can illustrate the performance and validity of our method.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Speed**} & \multicolumn{2}{c}{**Optimal**} & \multicolumn{2}{c}{**Emotional: HMC**} \\ \cline{2-5}  & **GLM** & **HMC** & **0.5** & **0.9** \\ \hline
17 & 49.2717 & 50.7372 & (52.2944, 50.7462, 49.0986) & (116.6369, 88.9605, 56.1986) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Optimal and emotional decisions: car data set.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Input**} & \multicolumn{2}{c}{**Optimal**} & \multicolumn{2}{c}{**Emotional: HMC**} \\ \hline \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & **GLM** & **HMC** & **0.5** & **0.9** \\ \hline \multirow{3}{*}{2} & 2 & 2.2919 & 2.5132 & (2.4987, 2.4989, 2.5021) & (2.1376, \(-\)0.3294, \(-\)1.0978) \\  & 4 & 7.3697 & 7.3154 & (7.3009, 7.3011, 7.3043) & (6.7160, 3.3936, 3.7315) \\  & 6 & 12.4475 & 12.1176 & (12.1031, 12.1033, 12.1065) & (11.2944, 7.1167, 8.5608) \\ \hline \multirow{3}{*}{4} & 2 & \(-\)0.6927 & \(-\)0.4624 & (\(-\)0.4914, \(-\)0.4911, \(-\)0.4847) & (\(-\)1.0696, \(-\)5.1515, \(-\)7.8567) \\  & 4 & 4.3851 & 4.3398 & (4.3108, 4.3111, 4.3175) & (3.5088, \(-\)1.4284, \(-\)3.0273) \\  & 6 & 9.4629 & 9.1420 & (9.1130, 9.1133, 9.1197) & (8.0873, 2.2946, 1.8020) \\ \hline \multirow{3}{*}{6} & 2 & \(-\)3.6773 & \(-\)3.4380 & (\(-\)3.4815, \(-\)3.4810, \(-\)3.4714) & (\(-\)4.2768, \(-\)9.9735, \(-\)14.6155) \\  & 4 & 1.4005 & 1.3642 & (1.3207, 0.3212, 1.3308) & (0.3016, \(-\)6.2505, \(-\)9.7862) \\ \cline{1-1}  & 6 & 6.4783 & 6.1664 & (6.1229, 6.1234, 6.1330) & (4.8801, \(-\)2.5275, \(-\)4.9569) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Optimal and emotional decisions: simulation data.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Estimated**} & \multicolumn{2}{c}{**Confidence Interval: HMC**} \\ \cline{2-5}  & **GLM** & **HMC** & **50\%** & **90\%** \\ \hline \(\beta_{0}\) & \(-\)17.5791 & \(-\)2.2399 & (\(-\)3.0122, \(-\)1.7071) & (\(-\)3.4520, \(-\)0.7613) \\ \hline \(\beta_{1}\) & 3.9324 & 3.1163 & (2.9993, 3.2496) & (2.8191, 7.2629) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Estimated parameters and intervals: car data set.