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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|Diverging Connection: Common Cause

Consider the example of a diverging connection shown in Figure $7.12$. Any evidence about the train being delayed, $A$, is transmitted to both Martin late, $B$, and Norman late, $C$.

For example, if we have hard evidence that increases our belief the train is delayed, then this in turn will increase our belief in both Martin being late and Norman being late. This is shown in Figure 7.13.

But we want to know whether information about $B$ can be transmitted to $C$ (and vice versa). Suppose we have no hard evidence about $A$ (that is, we do not know for certain whether the train is delayed). If we have some evidence that Martin is late, $B$, then this increases our belief that the train is delayed $A$ (here we reason in the opposite direction of the causal arrow using Bayes’ theorem). But the increased belief in the train being delayed in turn increases our belief in Norman being late. In other words, evidence about $B$ (Martin late) is transmitted through to $C$ (Norman late). This is shown in Figure 7.14. Of course, by symmetry, we can similarly conclude that evidence entered at $C$ is transmitted to $B$ through $A$.However, suppose now that we have hard evidence about $A$; for example, suppose we know for certain the train is delayed as shown in Figure 7.15. This evidence will increase our belief about Norman being late, $C$. But now any evidence about Martin being late will not change our belief about Norman being late; the certainty of $A$ blocks the evidence from being transmitted (it becomes irrelevant to $C$ once we know $A$ for certain).

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Converging Connection: Common Effect

Consider the example of a converging connection shown in Figure 7.16.
Clearly any evidence about either the train being delayed $(B)$ or Martin oversleeping $(C)$ will lead us to revise our belief about Martin being late $(A)$. So evidence entered at either or both $B$ and $C$ is transmitted to $A$ as shown in Figure 7.17.

However, we are concerned about whether evidence can be transmitted between $B$ and $C$. If we have no information about whether Martin is late, then clearly whether Martin oversleeps and whether there are train delays are independent. In other words if nothing is known about $A$ then A’s parents ( $B$ and $C$ ) are independent, so no evidence is transmitted between them.

However, suppose we have some information about $A$ (even just uncertain evidence) as shown in Figure 7.18. For example, suppose that Martin usually hangs up his coat in the hall as soon as he gets in to work. Then if we observe that Martin’s coat is not hung up after 9:00 a.m. our belief that he is late increases (note that we do not know for certain that he is late; we have uncertain evidence as opposed to hard evidence because on some days Martin does not wear a coat). Even this uncertain evidence about Martin being late increases our belief in both Martin oversleeping, $B$, and train delay, $C$. If we find out that one of these is false the other is more likely to be true. Under these circumstances we say, therefore, that $B$ and $C$ are conditionally dependent on $A$ (or, equivalently, that they are $d$-connected given A).

It follows that in a converging connection evidence can only be transmitted between the parents $B$ and $C$ when the converging node $A$ has received some evidence (which can be hard or uncertain). A proof is shown in Box $7.8$.

# 贝叶斯分析代考

## 有限元方法代写

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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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