## 4 Methodology for Model Construction
### Type of Learning Method Based on a Baysian Network  
A Bayesian network is a tool that allows for the expression of the joint probability distribution between variables, while providing explanations in both quantitative and qualitative terms for a given set of discrete random variables that can be observed and measured [38].  
In quantitative terms, the Bayesian network explains the parts where the conditional probabilities between variables are specified, and in qualitative terms, it explains the parts expressing conditional independence or dependence between the variables [39].  
A Bayesian network can be described using a model that helps determine the relationship between the variables and the data given for a specific variable and the probability that the relationship occurs. The Bayesian network consists of two parts: BN = f(G,D), where G indicates a directed acyclic graph composed of nodes and arcs. The nodes are the variables \(X_{1}\),..., \(X_{n}\) in the data set, whereas the arcs indicate direct dependencies between the variables. The graph G then encodes the independence relationships in the domain under investigation. The first task when learning a Bayesian network is to find the structure G of the network. G is estimated through iterative structural design learning. The second part, D, represents the probability distribution. In the probability distribution, \(x_{i}\), the value of the variable \(X_{i}\), which indicates the parameter in the form of \(D_{X_{i}}|=P_{B}(x_{i}\prod X_{i})\), can be given when the combination of the variable \(X_{i}\) and the direct parameter variable \(\prod X_{i}\) is given, where \(\prod X_{i}\) represents the set of direct parents of the variable \(X_{i}\) in G. Thus, a joint distribution is obtained as follows:  
\[P_{B}(X_{1},X_{2},\ldots,X_{n})=\prod_{i=1}^{n}P_{B}(x_{i}|\prod X_{i}) \tag{1}\]  
where,  
\(P_{B}\): Combined random variable of random variable \(X\)  
\(P_{B}(x_{i}|\prod X_{i})\): Conditional probability distribution of random variable \(X\).  
The naive Bayesian network (NBN), which is the most general form, was developed as a popular network construction algorithm. Given that parametric learning of the model does not require complex iterative processes and effectively avoids the subjectivity of expert judgment, it can reduce the complexity of the composition. However, assumptions regarding NBN construction are sometimes too hypothetical to be realistic. To improve the performance of the NBN, the structure is augmented with links between attributes or factors. This type of structure that does not require independence between attributes is called an augmented BN (ABN). In addition, if a class variable has no parent, each attribute has a class variable and a maximum of one other attribute as a parent. The ABN under this condition is called the tree augmented naive Bayes (TAN). TAN is a Bayesian network with the assumption that there is a tree-type relationship between child nodes in order to  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Category** & **Average** \\ \hline AADT (5-year average) & 17,217.2 vehicle/day \\ \hline Road surface condition & dry0: 72.6\%, damp: 27.4\% \\ \hline Daytime/nighttime & nighttime: 48.0\%, daytime: 52.0\% \\ \hline Weekends/weekdays & weekdays: 65.0\%, weekends: 35.0\% \\ \hline Compliance status of minimum radius of curve & Compliance: 86.1\%, not compliance: 13.9\% \\ standard & \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._relax the assumption of NBN with sweeping independence between the child nodes [40]. Compared to NBN and data-driven network construction approaches, TAN has is more competitive and accurate [40, 41]. Thus, TAN has a wide range of applications in various risk studies [22, 42] in the field of transportation.