## 7 Conclusions  
This study makes use of the advantages of hierarchical Bayesian inference models to quantify the levels of safety in European airspace. The study has three objectives: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Model 1**} \\ \hline
**ANSP** & **K4** & **1/K4** & **ANSP** & **K4** & **1/K4** \\ \hline K4[12] & 78.72 & 0.01270363 & K4[11] & 995.88 & 0.00100414 \\ \hline K4[9] & 335.54 & 0.00298031 & K4[16] & 996.41 & 0.0010036 \\ \hline K4[18] & 910.07 & 0.00109882 & K4[10] & 997.51 & 0.0010025 \\ \hline K4[22] & 938.38 & 0.00106567 & K4[5] & 998.61 & 0.00100139 \\ \hline K4[6] & 940.35 & 0.00106344 & K4[15] & 999.38 & 0.00100062 \\ \hline K4[29] & 967.66 & 0.00103342 & K4[2] & 1000.17 & 0.00099983 \\ \hline K4[19] & 983.35 & 0.00101693 & K4[14] & 1001.45 & 0.00099855 \\ \hline K4[8] & 985.24 & 0.00101498 & K4[13] & 1001.74 & 0.00099826 \\ \hline K4[27] & 987.27 & 0.00101289 & K4[17] & 1002.27 & 0.00099774 \\ \hline K4[28] & 988.36 & 0.00101177 & K4[7] & 1003.27 & 0.00099674 \\ \hline K4[26] & 991.03 & 0.00100905 & K4[4] & 1004.16 & 0.00099585 \\ \hline K4[25] & 992.95 & 0.0010071 & K4[21] & 1006.19 & 0.00099385 \\ \hline K4[1] & 993.41 & 0.00100664 & K4[3] & 1011.88 & 0.00098826 \\ \hline K4[20] & 994.45 & 0.00100558 & K4[24] & 1012.89 & 0.00098727 \\ \hline K4[23] & 995.47 & 0.00100455 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Deviation of each ANSP with respect to influence of complexity index in the number of SMIs for the overall European ATM system. * Generate predictive models that enable the number of losses of separation between aircraft in the airspace to be predicted using predictive variables such as the number of flight hours or the complexity of the airspace. * Estimate the general underlying safety level of European ATM systems. * Estimate how much each of the European ANSPs deviates from this general value. For this, four models were developed that combine a hierarchical approach with a regression model. These enable us to infer and predict the common rate of occurrence of SMIs, as well as the specific rates of occurrence for each ANSP. The models take two factors into consideration: the hierarchical relationship between the ANSPs and the generation of SMIs from predictors that represent the main local differences. The four models generally demonstrate good behavior. Model 4 is the most efficient and Model 2 the least efficient. For small values of SMIs, the Poisson model (Model 1) is more efficient, while for high values of SMIs the normal model (Model 4) is more accurate. For intermediate values, all models behave in a similar manner. The DIC values for Models 1 and 3 are similar. The original pieces of knowledge provided by this research can be summarized as:  
* The development of explanatory and predictive models for the number of SMIs as a function of the \"number of flight hours\", \"complexity score\", \"adjusted density\", and \"structural index\". * The models quantify the underlying safety level of European ATM and how much each of the European ANSPs deviates from this general value. * The contribution of the European ATM regulation to a reduced number of SMIs has been quantified as an overall EU ATM system performance. * The models explain and predict SMIs for 29 European ATM systems with common regulations and work procedures, but with different local circumstances. * The models are compatible with a very reduced set of data and able to integrate available expert prior information. * The models prove to be able to capture hierarchical dependences between parameters. The models developed have been found to be useful in explaining and predicting the safety performance of 29 European ATM systems with common regulations and work procedures, but with different circumstances and numbers of aircraft, each managing traffic of differing complexity. This study shows the usefulness of hierarchical structures when it comes to obtaining parameters that enable risk to be quantified effectively.