## 4 BBN Model Validation
### Model Validation Based on Diagnostic Inference  
Case \"Zlatni Zal\"--Based on the propositions in Section 2.2 and the accident report for \"Zlatni Zal\", the stepwise instantiation of evidence is introduced. First, forward propagation of the observed evidence of causal variables is performed and unobserved causal variable changes are collected. Then, backward propagation from the grounding variable is added. Again, unobserved variable changes are collected. Finally, diverging change \(\text{DR}(\text{X}_{1}^{\text{u}})\) from the Equation (8) is used to identify the factors \(\text{X}_{1}^{\text{u}}\) with consistently increasing change of the accident contributing causal parameter. The Lyapunov-based diverging change \(\text{DR}(\text{X}_{1}^{\text{u}})\) selects seven variables, as shown in Figure 11.  
The obtained results are interpreted with respect to the network structure, as shown in Figure 12. The selected causal variable that has the strongest causal contribution to grounding of \"Zlatni zal\" is \"loss of control\", supported by causal variables higher in the structure: \"AIS\", \"human error\", \"personal condition\", \"breakdown\", \"other distraction\", and \"maintenance\". All the parameters of the selected factors have negatively affecting states, e.g., \"loss of control\" state \"yes\", \"AIS\" state \"No\", \"human error\" state \"yes\", \"personal condition\" state \"bad\", etc. As explained in Section 2, due to modularity, BBN causes at different levels of the network can be treated as effects, which is exploited in a diagnostic interpretation mechanism that led to an accident. The propagation of information is observed in the bottom-up direction, and reasoning is as follows: it is known from the accident report that \"navigation in shallow water\" and \"special caution area\" cannot be accident contributory causal factors. Therefore, \"off course\" is the only remaining gate through which the propagation was possible. \"Off course\" could have been caused through three direct causal factors: \"loss of control\", \"navigational error\", and \"vessel damage\". The DR measure identified the \"loss of control\", which is strongly supported by \"AIS\" and \"human error\". Additional  
Figure 10: Model of the grounding of a small passenger ship “Cicero” according to the report on the maritime accident. weaker support of \"loss of control\" comes from \"breakdown\", \"other distractions\", and \"maintenance\". Figure 12 visualizes the accident-contributing candidates for \"Zlatni Zal\" in a model structure (the BBN structure of Figure 12 is created with Netica [19]). Case \"Cicero\"--Based on the propositions in Section 2.2 and the accident report for \"Cicero\", the stepwise instantiation of evidence is introduced, in a similar manner as in the \"Zlatni Zal\" case. The DR measure identified \"navigational error\" as the sole accident-contributing causal factor. Figure 13 visualizes the accident-contributing candidate for \"Cicero\" in a model structure. When the BBN causes at different levels of the network are observed as effects, and the information is observed in the bottom-up direction, the following inference is drawn: it is known from the accident report that \"navigation in shallow water\" and \"special caution area\" cannot be causal variables and therefore, \"off course\" is the only remaining gate through which the propagation was possible. \"Off course\" could have been caused through three direct causal variables: \"loss of control\", \"navigational error\", and \"vessel damage\". The DR measure identified the \"navigational error\". Figure 11: Candidate selection using the Lyapunov-based divergence measure. Figure 12: Visualization of the accident-contributing candidates for “Zlatni Zal”. Validation against two real world grounding cases has demonstrated the plausible predictive performance, and excellent explanatory performance of the developed model as the results are in accordance with the reported causes of marine casualties in the marine casualty report obtained by authorities.