## 5 Case Study
### Parametric Causality Inference and Anomaly Detection on a Real Satellite Telemetry Dataset
#### 5.2.4 Results and Discussion
**(a,b)** The multi-tier thresholds setting of the target parameter and WSP (the red dashed line is \((S)TU_{h},(S)TL_{l}\), the orange dashed line is the \((S)TU_{m},(S)TL_{m}\), and the blue dashed line is the \((S)TU_{l},(S)TL_{h}\)), and **(c)** the detection results of DCDSPOT. Figure 14: Thresholds setting and detection result of Q by DCDSPOT. **(a,b)** The multi-tier thresholds setting of the target parameter and WSP (the red dashed line is \((S)TU_{h_{r}}(S)TL_{l}\), the orange dashed line is the \((S)TU_{lm_{r}}(S)TL_{m}\), and the blue dashed line is the \((S)TU_{l_{r}}(S)TL_{h}\)), and **(c)** the detection results of DCDSPOT. Figure 13: Thresholds setting and detection result of D by DCDSPOT. **(a,b)** The multi-tier thresholds setting of the target parameter and WSP (the red dashed line is \((S)TU_{h_{r}}(S)TL_{l}\), the orange dashed line is the \((S)TU_{lm_{r}}(S)TL_{m}\), and the blue dashed line is the \((S)TU_{l_{r}}(S)TL_{h}\)), and **(c)** the detection results of DCDSPOT. Figure 15: Thresholds setting and detection result of T by DCDSPOT. (**a,b**) The multi-tier thresholds setting of the target parameter and WSP (the red dashed line is \((S)TU_{Hv},(S)TL_{J}\), the orange dashed line is the \((S)TU_{m},(S)TL_{m}\), and the blue dashed line is the \((S)TU_{l},(S)TL_{h}\)), and (**c**) the detection results of DCDSPOT. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Detection Method**} & \multicolumn{4}{c}{**Parameter: B**} & \multicolumn{4}{c}{**Parameter: D**} \\ \cline{2-9}  & **Pre (\%)** & **Rec (\%)** & **F1** & **T (s)** & **Pre (\%)** & **Rec (\%)** & **F1** & **T (s)** \\ \hline
3\(\sigma\) & **100** & 40.91 & 0.5806 & **1.3** & 93.87 & 10.24 & 0.1847 & **1.23** \\ LOF & 4.17 & 0.88 & 0.0145 & 3.8 & 24.85 & 1.37 & 0.026 & 3.31 \\ OCSVM & 70.92 & 60.35 & 0.6521 & 61 & 30.79 & 36.15 & 0.3325 & 83 \\ Isolation Forest & 70.77 & 60.23 & 0.6508 & 74 & 30.26 & 35.56 & 0.327 & 111 \\ biSPOT & 51.07 & 54.17 & 0.5257 & 193 & 57.67 & 11.63 & 0.1936 & 207 \\ biDSPOT & 60.65 & 61.11 & 0.6088 & 44 & **99.88** & 28.86 & 0.4480 & 51 \\ LSTM-VAE & 66.29 & 53.89 & 0.5945 & 342 & 55.69 & 11.45 & 0.19 & 301 \\ TCN & 56.84 & 57.44 & 0.5714 & 217 & 52.73 & 18.61 & 0.2752 & 244 \\ GAN & 48.43 & 54.94 & 0.5148 & 311 & 45.45 & 19.25 & 0.2705 & 375 \\ DCDSPOT & 87.91 & **89.02** & **0.8846** & 259 & 82.82 & **87.89** & **0.8528** & 265 \\ \hline \multirow{2}{*}{**Detection Method**} & \multicolumn{4}{c}{**Parameter: Q**} & \multicolumn{4}{c}{**Parameter: T**} \\ \cline{2-9}  & **Pre (\%)** & **Rec (\%)** & **F1** & **T (s)** & **Pre (\%)** & **Rec (\%)** & **F1** & **T (s)** \\ \hline
3\(\sigma\) & 84.41 & 6.81 & 0.1261 & **1.35** & **100** & 1.12 & 0.0222 & **1.07** \\ LOF & 25.25 & 1.19 & 0.0227 & 4.1 & 22.76 & 1.66 & 0.031 & 3.77 \\ OCSVM & 28.98 & 27.25 & 0.2809 & 73 & 71.64 & 32.05 & 0.4429 & 67 \\ Isolation Forest & 27.4 & 25.75 & 0.2655 & 96 & 40.39 & 19.29 & 0.2611 & 91 \\ biSPOT & 59.06 & 10.14 & 0.1730 & 212 & 93.17 & 13.19 & 0.231 & 199 \\ biDSPOT & **99.32** & 69.85 & 0.8202 & 63 & 84.51 & 2.87 & 0.0555 & 66 \\ LSTM-VAE & 56.08 & 10.97 & 0.1835 & 418 & 38.86 & 1.18 & 0.0229 & 335 \\ TCN & 55.69 & 7.99 & 0.1373 & 207 & **100** & 0.8 & 0.0168 & 236 \\ GAN & 51.06 & 10.69 & 0.1768 & 299 & 74.86 & 1.93 & 0.0376 & 327 \\ DCDSPOT & 81.84 & **91.77** & **0.8652** & 308 & 87.12 & **95.97** & **0.9133** & 318 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Anomaly detection performance of baseline methods and DCDSPOT.