### 统计代写|贝叶斯分析代写Bayesian Analysis代考|STAT4102

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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|The Crucial Independence Assumptions

Take a look again at the BN model of Figure $7.3$ and the subsequent calculations we used. Using the terminology of Chapter 5 what we have actually done is use some crucial simplifying assumptions in order to avoid having to work out the full joint probability distribution of:
(Norman late, Martin late, Martin oversleeps, Train strike) We will write this simply as $(N, M, O, T)$
For example, in calculating the marginal probability of $\operatorname{Martin}$ late $(M)$ we assumed that $M$ was dependent only on Martin oversleeps $(O)$ and Train strike $(T)$. The variable Norman late $(N)$ simply did not appear in the equation because we assume that none of these variables are directly dependent on $N$. Similarly, although $M$ depends on both $O$ and $T$, the variables $O$ and $T$ are independent of each other.

These kind of assumptions are called conditional independence assumptions (we will provide a more formal definition of this later). If we were unable to make any such assumptions then the full joint probability distribution of $(N, M, O, T)$ is (by the chain rule of Chapter 5)
$$P(N, M, O, T)=P(N \mid M, O, T) P(M \mid O, T) P(O \mid T) P(T)$$
However, because $N$ directly depends only on $T$ the expression $P(N \mid M, O, T)$ is equal to $P(N \mid T)$, and because $O$ is independent of $T$ the expression $P(O \mid T)$ is equal to $P(O)$.
Hence, the full joint probability distribution can be simplified as:
$$P(N, M, O, T)=P(N \mid T) P(M \mid O, T) P(O) P(T)$$
and this is exactly what we used in the computations.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Structural Properties of BNs

In $\mathrm{BNs}$ the process of determining what evidence will update which node is determined by the conditional dependency structure. The main formal area of guidance for building sensible BN structures therefore requires some understanding of different types of relationships between variables and the different ways these relationships are structured.

Generally we are interested in the following problem. Suppose that variable $A$ is linked to both variables $B$ and $C$. There are three different ways the links can be directed as shown in Figure 7.8. Although $B$ and $C$ are not directly linked, under what conditions in each case are $B$ and $C$ independent of $A$ ?

Knowing the answer to this question enables us to determine how to construct appropriate links, and it also enables us to formalize the different notions of conditional independence that we introduced informally in Chapter $6 .$

The three cases in Figure $7.8$ are called, respectively, serial, diverging, and converging connections. We next discuss each in turn.

Consider the example of a serial connection as shown in Figure 7.9. Suppose we have some evidence that a signal failure has occurred $(B)$. Then clearly this knowledge increases our belief that the train is delayed $(A)$, which in turn increases our belief that Norman is late $(C)$. Thus, evidence about $B$ is transmitted through $A$ to $C$ as is shown in Figure 7.10.

However, now suppose that we know the true status of $A$; for example, suppose we know that the train is delayed. Then this means we have hard evidence for A (see Box $7.5$ for an explanation of what hard and uncertain evidence are and how they differ).

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|The Crucial Independence Assumptions

$$P(N, M, O, T)=P(N \mid M, O, T) P(M \mid O, T) P(O \mid T) P(T)$$

$$P(N, M, O, T)=P(N \mid T) P(M \mid O, T) P(O) P(T)$$

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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。