统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|Non-deterministic CPT

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|Non-deterministic CPT

The binary state hypothesis is usually made while dealing with reliability or dependability analysis, as done in previous sections. Then, Boolean logic (OR, AND, XOR, NOT, etc.) defines the failure scenarios that lead to the undesired event as described by FT or equivalent representations. There is also the possibility of translatingalgebraic relations. In these situations, BN include deterministic CPT, i.e. conditional probabilities only in 0,1 .Nevertheless, BN models are able to consider non-deterministic CPT. Non-deterministic CPT is defined by conditional probabilities in ] $0,1[$. It means that the occurrence of a cause cannot produce the consequence at all. If the CPT is built by the database, then the non-deterministic CPT arrives when the occurrences of some parent states do not produce the same occurrence of the child state. When the CPT is built by an analyst, the non-deterministic CPT translates the analyst’s inability to define a strict logical relation between the parents and the considered variable. The problem occurs if the expert is unsure about the relation or if he suspects that other non-modeled elements influence the variable considered.

When the CPT is defined from a large dataset, a learning algorithm solves the problem easily. Three principal algorithms exist: counting [HEC 96, KRA 98], expectation-maximization [LAU 95] and gradient descent [BIN 97]. The previous case considers a general case where all conditional probabilities are estimated in the interval $[0,1]$. The problem of learning CPT arises when there is a small dataset [ONI 01]. This case is usually too incommodious to be defined by an expert. If there is a known relation between parents and the variable considered, this relation may simplify the expert’s work. Henrion [HEN 89] talks about independence of the causal influence (ICI) models based on the assumption of ICI of the parents. This assumption leads to the number of parameters needed to build the CPT, proportional to the number of parents. A further distinction is made between:

• noisy ICI models;
• leaky ICI models (i.e. an extension of the formers);
• probabilistic ICI.

统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|Industrial applications

Over the past few years, several modeling approaches have dealt with a global view of risks, accounting for technical aspects while being immersed in human, organizational and environmental contexts. [PAT 96] developed the system-action-management (SAM) approach and [SVE 02] highlighted the importance of considering different actors in the risk analysis of an industrial system through a graphical representation of causal flow of accidents (AcciMap). Moreover, [PAP 03] developed the I-Risk method that can account for both technical and organizational characteristics in system risk analysis for the chemical industry. [PLO 04], with MIRIAM1-ATHOS2, evaluated major risk management systems examining technical, human and organizational factors. [CHE 06] focused on the representation of accidental scenarios via the bowtie formalism to facilitate the organizational learning process and [MOH 09] proposed a means of carrying out probabilistic safety studies by taking organizational factors into account.

A recent method was proposed during an academic/industrial collaboration by EDF, INERIS (L’Institut National de l’Environnement Industriel et des Risques) and CRAN (Research Center for Automatic Control of Nancy) [LÉG 09]. This method is called integrated risk analysis. It focuses on a unified risk modeling. The model is multidisciplinary and generic. The generic property comes from a bowtie node for the technical parts, which serves as a basis from which to integrate knowledge about the human, organizational and environmental contexts through the barriers’ efficiency that mitigate the influences of basic events on the consequences of accidental situations.

This modeling methodology has been applied to the assessment of risks in an industrial power plant and, more precisely, to the assessment of technical, human and organizational mitigation actions [LÉG 08a]. The unified model is structured based on the organizational level, the human actions level and their impacts (inhibition) on the propagation of causes and consequences into the bowtie model [LÉG $08 \mathrm{a}$, LÉG 08 ,

LÉG 08b]. The model structure is given in Figure 2.13. The model obtained is used to estimate the occurrence probability of some risk scenarios and to assess the efficiency of barriers on risk reduction. In the risk management process [IEC 09], an engineer can use the model to identify the weaknesses of the socio-technical system and act accordingly to keep the risk criticality below an acceptable level. For the computation part, the model is based on a BN because it combines knowledge and observations to simulate scenarios and to identify weaknesses.

The reader can find an application of this BN-based modeling methodology on a chemical process in [LÉG 09]. In this application, 80 variables are considered. In [DUV 12], a critical system of a power plant is modeled with approximately 110 variables. This latter model is presented in Figure 2.14. The large number of variables in such a model means that only specialists are qualified to understand and perform simulations to characterize risks.

统统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|Conclusion

This chapter illustrates how BN can solve the modeling problems of dependability and risk analysis of complex systems. This formalism works well with usual Boolean approaches such as FT or RBD. The construction of BN models in such cases follows the same guidelines and gives the same results.

The construction can be automatic by enumerating the cut-sets or tiesets, whether minimal or not. Moreover, BN is well suited to modeling complex systems where dependencies between variables are not only deterministic.

Several BN structures are feasible for system dependability modeling. Model validation rests on the validation of the method used to build the model and confrontating the model with experiences by testing scenarios to validate the coherence of the model with well-known real cases.

Although BN provides a very compact model of large and complex problems, and makes it possible to handle hundreds of variables, some thousands of variables are needed for large industrial systems. In this case, the BN reach their limits. When the number of variables becomes too large, i.e. if the model cannot be supported in the memory of the computer that handles it, it is then necessary to use a more suitable modeling formalism.

统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|Non-deterministic CPT

• 嘈杂的 ICI 模型；
• 泄漏的 ICI 模型（即前者的扩展）；
• 概率 ICI。

统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|Industrial applications

EDF、INERIS（L’Institut National de l’Environnement Industriel et des Risques）和 CRAN（Nancy 自动控制研究中心）[LÉG 09] 在学术/工业合作期间提出了一种最近的方法。这种方法称为综合风险分析。它侧重于统一的风险建模。该模型是多学科和通用的。通用属性来自技术部分的领结节点，作为基础，通过屏障的效率整合有关人类、组织和环境背景的知识，从而减轻基本事件对意外情况后果的影响。

LÉG 08b]。模型结构如图 2.13 所示。得到的模型用于估计一些风险情景的发生概率，并评估障碍降低风险的效率。在风险管理过程 [IEC 09] 中，工程师可以使用该模型来识别社会技术系统的弱点，并采取相应的行动将风险严重性保持在可接受的水平以下。对于计算部分，该模型基于 BN，因为它结合了知识和观察来模拟场景并识别弱点。

广义线性模型代考

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MATLAB代写

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