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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|贝叶斯分析代写Bayesian Analysis代考|Propagation in Bayesian Networks

When there are many variables and links, as in most real-world models, and where the number of states for each variable, is large, calculations become daunting or impossible to do manually. In fact, no computationally efficient solution for BN calculation is known that will work in all cases. This was the reason why, despite the known benefits of BNs over other techniques for reasoning about uncertainty, there was for many years little appetite to use BNs to solve real-world decision and risk problems.

However, dramatic breakthroughs in the late 1980s changed things. Researchers such as Lauritzen, Spiegelhalter, and Pearl published algorithms that provided efficient propagation for a large class of BN models. These algorithms are efficient because they exploit the BN structure, by using a process of variable elimination, to carry out modular calculations rather than require calculations on the whole joint probability model.
The most standard algorithm, which is explained informally in this section and formally in Appendix $\mathrm{C}$, is called the junction tree algorithm. In this algorithm, a BN is first transformed into an associated tree structure (this is the junction tree) and all of the necessary calculations are then performed on the junction tree using the idea of message passing. An example of a BN (the same one we used in Figure 7.7) and its associated junction tree is shown in Figure 7.20. In this case the BN itself was already a tree structure; a more interesting example is shown in Figure 7.21.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Building a BN Model

Building a $\mathrm{BN}$ to solve a risk assessment problem therefore involves the following steps (much of the rest of this book is concerned with more detailed guidelines on the various steps involved):

1. Identify the set of variables that are relevant for the problemYou should always try to keep the number down to the bare minimum necessary. For example, if your interest is in predicting and managing flood risk in a particular city close to a river, then relevant variables might be River water level, Rainfall, Quality of flood barrier, Flood, Availability of sandbags, Quality of emergency services, People drown, and Houses ruined. Note that your perspective of the problem will determine both the set of variables and the level of granularity. So, if you were a city official trying to assess the general risk to the city then having a single variable Availability of sandbags to represent the average availability over all households makes more sense than having a node for each individual household.
2. Create a node corresponding to each of the variables identified. This is shown in Figure 7.23. Note that in AgenaRisk you first need to decide if the node is discrete or continuous (continuous nodes are normally defined as simulation nodes-sidebar
Figure $7.24$ shows how to create discrete and simulation nodes).
3. Determine the node type. Depending on whether it is a discrete or continuous simulation node you will have different options for the node types as shown in Figure 7.25. For example: “Flood” could reasonably be a discrete Boolean node; “River Water level” could be a continuous interval simulation node; “Quality of flood barriers” could be a ranked node. The type you choose depends on your perspective (as we shall see later it will also be restricted by issues of complexity).
4. Specify the states for each non-simulation node. Having chosen the node type you can specify the names of states and (for non-Boolean nodes) the number of states. For example, “Quality of flood barriers” could have just three states-high, medium and low-or more as shown in Figure 7.26. Chapters 9 and 10 provide full details about selecting the type of variables and its set of states.
1. Identify the variables that require direct links. For example, River water level directly affects Flood and Flood directly affects Houses ruined but we do not need a direct link from River water level to Houses ruined because this link already exists through Flood. Earlier sections of this chapter, together with Chapter 8, provide guidance on this step. In AgenaRisk you use the link tool to create the identified links. This is demonstrated in Figure $7.27 .$

# 贝叶斯分析代考

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Building a BN Model

1. 确定与问题相关的变量集您应该始终尝试将数字保持在必要的最低限度。例如，如果您的兴趣是预测和管理靠近河流的特定城市的洪水风险，那么相关变量可能是河流水位、降雨量、防洪屏障的质量、洪水、沙袋的可用性、紧急服务的质量、人员淹死，房屋毁坏。请注意，您对问题的看法将决定变量集和粒度级别。因此，如果您是一名试图评估城市总体风险的城市官员，那么使用单个变量沙袋可用性来代表所有家庭的平均可用性比为每个家庭设置一个节点更有意义。
2. 创建一个对应于每个标识的变量的节点。如图 7.23 所示。请注意，在 AgenaRisk 中您首先需要确定节点是离散的还是连续的（连续节点通常定义为模拟节点-侧边栏
图7.24展示了如何创建离散和模拟节点）。
3. 确定节点类型。根据它是离散模拟节点还是连续模拟节点，您将有不同的节点类型选项，如图 7.25 所示。例如：“Flood”可以合理地是一个离散的布尔节点；“河流水位”可以是一个连续区间模拟节点；“防洪屏障的质量”可以是一个排名节点。您选择的类型取决于您的观点（正如我们稍后将看到的，它也会受到复杂性问题的限制）。
4. 指定每个非模拟节点的状态。选择节点类型后，您可以指定状态名称和（对于非布尔节点）状态数量。例如，“防洪屏障的质量”可能只有三个状态——高、中、低或更高，如图 7.26 所示。第 9 章和第 10 章提供了有关选择变量类型及其状态集的完整细节。
5. 确定需要直接链接的变量。例如，河流水位直接影响洪水，洪水直接影响房屋毁坏，但我们不需要从河流水位到房屋毁坏的直接链接，因为这种联系已经通过洪水存在。本章前面的部分以及第 8 章提供了有关此步骤的指导。在 AgenaRisk 中，您使用链接工具来创建已识别的链接。

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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。

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