Uncertain Evidence in Bayesian Networks: Presentation and Comparison on a Simple Example

Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis

Dynamic event tree (DET) is an important method in dynamic probabilistic risk assessment; however its real application is limited due to its heavy computation complexity and inconvenience to deal with dependent events. This paper aims at constructing Bayesian networks based on dynamic event tree, and solving the probability of each consequence by utilizing various exact and approximate inference algorithms in Bayesian networks. The dependencies between events, such as common cause failures, could be easily modeled in Bayesian networks. The comparison of the simulation results is carried out by an example in the end.

Bayesian network (BN) inference is an important statistical tool with additive symmetry. However, BN inference cannot deal with the uncertain, fuzzy, random, and conflicting information from experts’ knowledge in the process of conducting a risk assessment. To tackle this issue, a new fuzzy BN inference approach for risk assessments was proposed based on cloud model (CM), interval type-2 fuzzy set (IT2 FS), interval type-2 fuzzy logic system (IT2 FLS), modified Dempster–Shafer (D-S) evidence theory (ET), and Latin hypercube sampling (LHS) methods along the following lines. Firstly, CM was integrated into IT2 FS, and CM-based IT2 FS (CM-IT2 FS) was defined in the IT2 FLS. Secondly, modified D-S ET was utilized to determine the CM-IT2 FS-based a priori probabilities, and the CM-IT2 FS-based BN model was established. Thirdly, the CM-IT2 FS-based a priori probabilities were reduced to the CM-IT1 FS-based ones using a type reducer in the IT2 FLS, LHS was applied to propose a new fuzzy BN inference algorithm, and then, the new algorithm was used in a typical case to perform the fuzzy BN positive inference for risk prediction and the fuzzy BN reverse inference for risk sensitivity analysis. Finally, the BN inference results were analyzed using the proposed algorithm and the two common BN inference algorithms, and the effectiveness of the proposed approach was validated. It can be concluded that the proposed approach was both accurate and promising.

We suggest Darwinian networks (DNs) as a simplification of working with Bayesian networks (BNs). DNs adapt a handful of well-known concepts in biology into a single framework that is surprisingly simple, yet remarkably robust. With respect to modeling, on one hand, DNs not only represent BNs, but also faithfully represent the testing of independencies in a more straightforward fashion. On the other hand, with respect to two exact inference algorithms in BNs, DNs simplify each of them, while unifying both of them.

Based on system analysis of information security risk factors and evaluation process, aiming at the uncertainty information is difficult to quantify the evaluation process, Bayesian network inference algorithm, and combined with the inference rules of conditional probability matrix is given by expert knowledge of Bayesian network, the evaluation model of information security risk. Finally an instance of the risk assessment approach on the model is analyzed which demonstrates the rationality and feasibility of this method. So it provides a new method for information security assessment.

Novel recursive inference algorithm for discrete dynamic Bayesian networks

We present an efficient procedure for factorising probabilistic potentials represented as probability trees. This new procedure is able to detect some regularities that cannot be captured by existing methods. In cases where an exact decomposition is not achievable, we propose a heuristic way to carry out approximate factorisations guided by a parameter called factorisation degree, which is fast to compute. We show how this parameter can be used to control the tradeoff between complexity and accuracy in approximate inference algorithms for Bayesian networks.

Travel time uncertainty can have a significant impact on the performance of Intelligent Transportation Systems. Various applications such as routing or pricing can benefit from accurate estimations of travel times. In this thesis, we propose an approach that can estimate travel time distributions for any path in the road network using GPS data. We focus on situations when only sparse data is available: we consider a dataset that contains GPS trajectories from probe vehicles sampled on average with 1-minute intervals. We propose employing a novel Bayesian network inference algorithm and combining it with the Gaussian copula model. This allows us to estimate the marginal distributions and the covariance structure separately.

The discrete dynamic Bayesian network is a useful tool for modeling and inferring the time series progress,and it has wide modeling application value.But its inference algorithm needs improving.Concerning the shortcomings of the discrete dynamic Bayesian network,such as its inference algorithm is hard to understand,hard to program and running slowly,this paper proposed the most suitable storage data structure of the discrete dynamic Bayesian network,deduced the fast inference algorithm for the discrete dynamic Bayesian network,and verified the inference algorithm for the discrete dynamic Bayesian networks through a sample.

A hierarchical fuzzy Bayesian network model for situation assessment is developed in the paper, which includes two layers: the top layer serving as a fusion center, the bottom layer as the continuous data discretization. In this model, Bayesian network (BN) is integrated with the fuzzy theory, which can generalize the continuous variable to fuzzy variable in BN. The fuzzy theory is utilized to partition the value of continuous variable into fuzzy state, which forms the soft evidence for Bayesian network. The inference mechanism of the model is given, through which the continuous and discrete data can be fused. As an example, an air strike scenario is simulated and analyzed to illustrate the functionality of the proposed model.

Bayesian belief networks (BBNs) are graphical tools for reasoning with uncertainties (see Chap. 7). They can be used to combine expert knowledge with hard data and making sense of uncertain evidence. The computation of Bayesian inference is complex. In this chapter, we provide a step-to-step guide of how to construct and use Bayesian networks by using Netica software.

Space launch projects are extremely risky, and any equipment failure or human error may lead to disastrous consequences. Probabilistic risk assessment (PRA) is beneficial to qualitative analysis of risk, but it has not been paid enough attention in risk analysis for space launch systems (SLSs). Compared with most qualitative risk analysis in this field, this paper proposes a risk analysis framework based on Bayesian network (BN) with fuzzy method, which is suitable for probabilistic risk analysis of SLS. This method establishes a risk analysis model of SLS based on statistics and expert experience and reduces the uncertainty of the model by using fuzzy theory. By predicting the system risk probabilities, diagnosing the key risk causes, determining the risk conduction path, and performing a sensitivity analysis, the proposed risk analysis framework is aimed at alleviating this drawback to deal more effectively with the uncertainties in the field of space launches. A case study of space launches demonstrates and verifies the proposed method, and it also provides guidance for similar engineering projects.

Risk analysis of collision accidents during underway STS berthing maneuver through integrating fault tree analysis (FTA) into Bayesian network (BN)

With the advent of Web 3.0 era, the number and complexity of Web pages in Bayesian networks have shown an explosive growth trend. Accompanying this is the geometric growth of information contained in Web pages. Web text data in Bayesian networks usually hide rich knowledge and rules of user value. However, due to the semi-structured, real-time and discrete characteristics of Web text data, it is difficult for users to obtain the knowledge they need directly from such complex data sets. The emergence of fuzzy mathematics provides a good research idea and method for solving such problems. It can use the idea of fuzzy mathematics to analyze the practical problems in text data. Therefore, how to effectively mine the Web text data information and knowledge that users really care about from Bayesian network, and present it in a way that users can understand, it is a very popular research topic at present. In this paper, we select the text of Bayesian network: microblog data for experiments. User data model of microblog is established by using relevant knowledge of fuzzy theory. The concept of fuzzy measure is introduced to calculate the non-additive measure value under the interaction relationship between the detection indicators. Determine the membership function relationship between the detection user and the text data, calculate the integral values of Choquet integral, Sugeno integral and Wang integral of the membership function under the non-additive measure, the final valuable web text data is judged by integral value. On the basis of the above research contents, the research results of Web text mining technology and fuzzy arithmetic mathematics are combined, design and implement information acquisition and analysis for Bayesian network community. The recall rate obtained by the experimental method in this paper is as low as 4%, and tends to be more stable.

Evidence-based volcanology: application to eruption crises