# Bayesian-Based Traffic Safety Evaluation Study for Driverless Infiltration
## 2 Materials and Methods
### Determining Bayesian Network Parameters  
#### 2.3.1 Leaky Noisy-OR Gate Extended Model  
When applying a Bayesian network, how to obtain the network parameters corresponding to the risk of driverless driving is an important problem that needs to be solved urgently. If there is a large number of complete datasets, you can directly build a BN model to obtain network parameters from the data set. For example, the Stochastic Approximate Monte Carlo method (SAMC), Maximum Likelihood Estimation (MLE), etc., are used. However, these methods require a large number of data samples, and the research mainly focuses on \(\beta\) distribution and binomial distribution, which have certain limitations. Due to the late start of China's artificial intelligence technology, the exploration of driverless technology is still in the primary stage, and there is not a complete risk case base. Atpresent, it is still necessary to rely on expert knowledge and historical experience to obtain the Bayesian network parameters, and the Leaky Noisy-OR-Gate model is a method to solve this kind of problem. The method in the knowledge of the network structure, and the expert knowledge, can approximate the conditional parameters of Bayesian network by Leaky Noisy-OR Gate model. The Noisy-OR Gate model can be used to describe the internal relationship between n variables \(X_{1}\), \(X_{2}\),..., \(X_{n}\) and the result Y they influence. The Bayesian network based on the Leaky Noisy-or Gate model also needs to meet the following three conditions:  
* Each node in the network is a binary discrete variable with 2 states, assuming they are true value (1) and false value (0). * The parent node of any node Y is \(X_{1}\), \(X_{2}\),..., \(X_{n}\), then \(X_{1}\), \(X_{2}\),..., \(X_{n}\) should be independent of each other. * Each variable is enough to cause the result Y to occur when other variables are false (0). At this time, only \(X_{i}\) (\(i\) = 1, 2,..., \(n\)) is 1, while other parent nodes are 0. The probability that Y takes the value 1 is \(P_{i}\), as shown in Equation (4). \[P_{i}=\mathrm{P}\big{(}\mathrm{Y}\big{|}\overline{X_{1}},\,\overline{X_{2}}, \,\,X_{i},\ldots,\,\,\overline{X_{n}}\big{)} \tag{4}\]  
Then \(P_{1}\),..., \(P_{i}\),..., \(P_{n}\) determine the other terms \(X\) in the conditional probability table for node Y, as shown in Equation (5). \[\mathrm{P}(\mathrm{Y}\mid X_{n})=1-\prod_{i:X_{i}\in X_{p}}(1-P_{i}) \tag{5}\]  
where \(X_{n}\) is the set of Y parent node values, \(X_{p}\) is a subset of \(X_{n}\), and the subset consists of parent nodes whose values are true. As there will be some other unknown factors that will affect node Y in the actual driverless risk, Henrion proposed the concept of leaky probability. The conditional probability modification model of the parent nodes n variables \(X_{1}\), \(X_{2}\),..., \(X_{n}\) with the same influence factor child node Y produced by them, which is the Leaky Noisy-OR-Gate extension model, assuming that Y (child node) has 2 mutually independent parent nodes: \(X_{i}\) and \(X_{all}\) (i.e.,  
Figure 3: Bayesian network structure for driverless risk indicators. factors other than \(X_{i}\) are merged into \(X_{all}\)), \(P_{i}\) and \(P_{all}\) are the connection probabilities of \(X_{i}\) and \(X_{all}\), as shown in Equations (6) and (7).