An Overview of Bayesian Network Applications in Uncertain Domains <s> C. Bayesian Networks Learning <s> This paper presents an efficient computational method for performing sensitivity analysis in discrete Bayesian networks. The method exploits the structure of conditional probabilities of a target node given the evidence. First, the set of parameters which is relevant to the calculation of the conditional probabilities of the target node is identified. Next, this set is reduced by removing those combinations of the parameters which either contradict the available evidence or are incompatible. Finally, using the canonical components associated with the resulting subset of parameters, the desired conditional probabilities are obtained. In this way, an important saving in the calculations is achieved. The proposed method can also be used to compute exact upper and lower bounds for the conditional probabilities, hence a sensitivity analysis can be easily performed. Examples are used to illustrate the proposed methodology. <s> BIB001 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> C. Bayesian Networks Learning <s> Identifying interactions among brain regions from structural magnetic-resonance images presents one of the major challenges in computational neuroanatomy. We propose a Bayesian data-mining approach to the detection of longitudinal morphological changes in the human brain. Our method uses a dynamic Bayesian network to represent evolving inter-regional dependencies. The major advantage of dynamic Bayesian network modeling is that it can represent complicated interactions among temporal processes. We validated our approach by analyzing a simulated atrophy study, and found that this approach requires only a small number of samples to detect the ground-truth temporal model. We further applied dynamic Bayesian network modeling to a longitudinal study of normal aging and mild cognitive impairment — the Baltimore Longitudinal Study of Aging. We found that interactions among regional volume-change rates for the mild cognitive impairment group are different from those for the normal-aging group. <s> BIB002 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> C. Bayesian Networks Learning <s> Bayesian approaches to learn the graphical structure of Bayesian Belief Networks (BBNS) from databases share the assumption that the database is complete, that is, no entry is reported as unknown. Attempts to relax this assumption involve the use of expensive iterative methods to discriminate among different structures. This paper introduces a deterministic method to learn the graphical structure of a BBN from a possibly incomplete database. Experimental evaluations show a significant robustness of this method and a remarkable independence of its execution time from the number of missing data. <s> BIB003
Once the nodes and their states to be modeled have been identified, a BN can be constructed in two ways. First, manual construction of BN is completely dependent upon expert knowledge. In this structure learning process, causal influence with conditional independence of nodes is considered as shown in Fig. 4 . Second, automatic or semi-automatic BNs are learnt through algorithms in knowledge discovery procedure in large datasets. These algorithms determine the independence or dependence relationship discovery among nodes. The potential outcome of learning BN structure refers to the investigation of hidden structure that conventional statistical methods fail to identify. A number of readily available tools can be utilized to learn BN structure using search-and-score-based algorithm and constrained-based-algorithms. A scoring metric is used in learning the best model structure with the use of Bayesian Knowledge Discoverer (BKD) BIB003 and Bayesian Lab BIB001 . On the other hand, a constraint-based algorithms finds the best possible BN structure by discovering overall conditional dependencies and independencies with the support of HUGGIN  , BN Power Constructor, Power Predictor BIB002 , 67], [68] , or TETRAD [69] . The constraint-based algorithms use domain knowledge in specifying relationships among variables.