统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|Modeling Formalism of the Structure

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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|Function of Boolean Systems

One of the principle characteristics of modeling Boolean stucture function using BN is the ability to construct models from knowledge without technical expertise regarding computing algorithms. Nevertheless, this advantage can be a source of doubt about the computing results obtained from BN models. Formally, the numerical results are exact and the question of validity should concern only the quality of the model built by the analyst and/or the representativeness of data used to learn the parameters. Therefore, it is very important to use a structured modeling approach to obtain a model that better corresponds to reality.

From a practical point of view, there is often a lack of data to inform models in reliability estimation, risk analysis and maintenance optimization. It is often impossible to fully define the joint distribution defining all situations and their associated probabilities. As a result, modeling tools require the use of expert judgments to build structured models [CEL 06]. The BN modeling practiced in this book is presented in this spirit.

BN is a powerful modeling tool as it can combine knowledge of different kinds. This combination is allowed by the probabilistic representation and the combination of state of affairs. The model structure as well as the estimation of the model parameters can be built either automatically or manually from: data from feedback experiences; expert judgments based mainly on logical rules (not necessarily Boolean logic); equations; and databases of the system states or observations. By using objective or subjective probabilities, a BN can formalize causal relations or dependences/independences between variables. For instance, BN can model the effect of maintenance actions carried out by humans on a technical system (see [MED 11]) as well as the effect of defense barriers on risk analysis (see [LÉG 09]).

As previously discussed, BN are well-suited to modeling the structure function of system reliability. This modeling approach is based mainly on statistical knowledge and uses a combination of data and knowledge of qualitative causal relations to describe conditional dependencies between variables. The structure function is used in dependability analysis to model the propagation of failure events, degradation and alteration of the system [VIL 88, COC 97, COR 75 , GER 00]. BN clearly helps in understanding the system behavior, thanks to the inference algorithm that propagates the observations (evidence) of the system and its components.

统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|BN models in the Boolean case

Let us consider the binary state hypothesis. The BN model can be compared with FT, RBD, cut-sets and tie-sets. In this section, the risk analysis bowtie model is also introduced and a BN representation is given. This model has been used successfully in industrial applications [LÉG 09, FAL 12].

For the sake of illustration, this section focuses on the flow distribution system: the three-valve system, given in Chapter 1 in Figure 1.2. The RBD of this system is illustrated in Figure 2.1. The mission of the system is to distribute the flow. Contrary to Chapter 1 , the binary state hypothesis is made. Thus, the components have two states: $x_{i}=0$ if the valve $i$ is working and allows the flow to go through the valve; and $x_{i}=1$ if the valve $i$ does not allow the flow to go through the valve – the valve is then considered broken. The probability distributions of $x_{i}$ are given in Table 2.1. The system is modeled by the variable $y: y=0$ if the system accomplishes its mission; and $y=1$ if the system is unable to accomplish its mission.

统统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|BN model from cut-sets

The cut-sets represent the malfunction scenarios of the system. Based on the RBD illustrated in Figure 2.1, three cut-sets can be isolated:
\begin{aligned} &C_{1}=\left{x_{1}\right} \ &C_{2}=\left{x_{2}, x_{3}\right} \ &C_{3}=\left{x_{1}, x_{2}, x_{3}\right} \end{aligned}
The system works if no cut-set occurs or conversely the system fails if at least one of the cut-sets occurs. This property is due to the Boolean nature of the components. The BN model of reliability based on these three cut-sets is shown in Figure 2.2.

Let us consider the probability distributions of the components’ states given in Table $2.1$ and the conditional probability tables of each of the cut-sets based on a deterministic equation. The CPT of cut-set $C_{2}$ is given in Table $2.2$ and the CPT for $y$ in Table $2.3$ for the sake of illustration.

The dependability engineer knows that it is efficient to compute the reliability directly with minimal cut-sets, i.e. cut-sets that do not include other cut-sets. Thus, equation [2.2] becomes equation [2.3] and consequently the $\mathrm{BN}$ model is reduced, as shown in Figure $2.3$.

统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|Function of Boolean Systems

BN 是一个强大的建模工具，因为它可以结合不同种类的知识。这种组合是由概率表示和事态的组合所允许的。模型结构以及模型参数的估计可以自动或手动构建：来自反馈经验的数据；专家判断主要基于逻辑规则（不一定是布尔逻辑）；方程；和系统状态或观察的数据库。通过使用客观或主观概率，BN 可以形式化变量之间的因果关系或依赖/独立。例如，BN 可以模拟人类进行的维护操作对技术系统的影响（参见 [MED 11]）以及防御障碍对风险分析的影响（参见 [LÉG 09]）。

统统计代写|贝叶斯网络概率解释代写Probabilistic Reasoning With Bayesian Networks代考|BN model from cut-sets

\begin{对齐} &C_{1}=\left{x_{1}\right} \ &C_{2}=\left{x_{2}, x_{3}\right} \ &C_{3}=\left{ x_{1}, x_{2}, x_{3}\right} \end{对齐}\begin{对齐} &C_{1}=\left{x_{1}\right} \ &C_{2}=\left{x_{2}, x_{3}\right} \ &C_{3}=\left{ x_{1}, x_{2}, x_{3}\right} \end{对齐}

广义线性模型代考

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MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。