_algorithms_  
Editorial for the Special Issue on \"Bayesian Networks:  
Inference Algorithms, Applications, and Software Tools\"  
[PERSON]  
Computer Science Institute, Dipartimento di Scienze e Innovazione Tecnologica, Universita del Piemonte Orientale, 15121 Alessandria, Italy; [EMAIL_ADDRESS]  
In the field of Artificial Intelligence, _Bayesian Networks_ (BN) [1] are a well-known framework for reasoning under uncertain knowledge. BNs have been applied in a wide range of real-world domains, such as medical diagnosis, forensic analysis, dependability assessment, risk management, etc. With respect to other types of models, BNs provide relevant advantages: at the modelling level, the compact representation of the joint distribution of the system variables leads to the factorization of the set of possible states, avoiding the generation of the complete state space of the system; at the analysis level, inference algorithms can compute the probability distribution of any variable, possibly conditioned on the observation of the value (state) of other variables, so that predictive and diagnostic measures can be easily evaluated. During the years, BNs have been extended in order to increase their modelling and analysis power; for instance, _Dynamic Bayesian Networks_ (DBN) and _Continuous-Time Bayesian Networks_ take time into account, _Hybrid Bayesian Networks_ deal with both discrete and continuous variables, _Decision Networks_ (DN) contain decision nodes and value nodes. This Special Issue covers a range of case studies examined by means of BNs and their extensions. DBNs are exploited for the risk assessment of a nuclear reactor in [2]. This infrastructure belongs to the class of _Complex Engineering Systems_ (CES) and DBNs enable the forward and backward inference of system states, diagnosing current system health, and forecasting future system prognosis. Simulated accident sequence data are used as evidence during DBN inference; the results can serve as a training tool for CES operators to better prepare for accident scenarios. Autonomous vehicles, taking the environmental context into account, are another application field documented in [3], where BNs help in _Fault Detection Isolation and Recovery_ (FDIR) in real-time conditions. The models are automatically generated from _Failure Mode and Effects Analysis_ (FMEA) and operate online for autonomous vehicles. Then, in the safe mission planning of _Unmanned Aerial Vehicles_ (UAV), DNs are experimented as decision-making models; several realistic examples show the benefits. A BN can be constructed by means of parameter and structure learning from data, as discussed in [4]. When data are incomplete, learning is usually implemented with the _Expectation-Maximization_ (EM) algorithm computing the relevant sufficient statistics by belief propagation, or with the _Structural Expectation-Maximization_ (Structural EM) algorithm building the network structure from those sufficient statistics. Since practical implementations often impute missing data to compute sufficient statistics, the impact of using imputation instead of belief propagation, is investigated on the quality of the resulting BNs. Given synthetic data, reference BNs, and several scenarios, the better approach is recommended according to the characteristics of the data. As a result, a _Decision Tree_ (DT) is built to guide practitioners in choosing the EM algorithm. Another work about machine learning is presented in [5] and deals with the problem of traffic barrier crashes, with the goal of identifying and optimizing the heights of the barriers, based on the monetary saving and the reduction of frequency and severity of crashes. The paper presents an empirical cost-benefit analysis based on _Bayesian hierarchical machine learning_ technique, where a hierarchical model is employed to provide a flexible way of addressing the problem. This work is extended in [6] where _Finite Mixture Model_ (FMM) is used to find the distribution parameters characterizing the observation dataset.