### 统计代写|贝叶斯网络代写Bayesian network代考|PHYS4016

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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|贝叶斯网络代写Bayesian network代考| Train-Use Survey

Consider a simple, hypothetical survey whose aim is to investigate the usage patterns of different means of transport, with a focus on cars and trains. Such surveys are used to assess customer satisfaction across different social groups, to evaluate public policies and to improve urban planning. Some real-world examples can be found, for instance, in Kenett et al. (2012).

In our current example we will examine, for each individual, the following six discrete variables (labels used in computations and figures are reported in parenthesis):

• Age (A): the age, recorded as young (young) for individuals below 30 years old, adult (adult) for individuals between 30 and 60 years old, and old (old) for people older than 60 .
• Sex (S): the biological sex, recorded as male (M) or female (F).
• Education (E): the highest level of education or training successfully completed, recorded as up to high school (high) or university degree (uni).
• Occupation (0): whether the individual is an employee (emp) or a selfemployed (self) worker.
• Residence (R): the size of the city the individual lives in, recorded as either small (small) or big (big).
• Travel (T): the means of transport favoured by the individual, recorded either as car (car), train (train) or other (other).
• In the scope of this survey, each variable falls into one of three groups. Age and Sex are demographic indicators. In other words, they are intrinsic characteristics of the individual; they may result in different patterns of behaviour but are not influenced by the individual himself. On the other hand, the opposite is true for Education, Occupation and Residence. These variables are socioeconomic indicators and describe the individual’s position in society. Therefore, they provide a rough description of the individual’s expected lifestyle; for example, they may characterise his spending habits and his work schedule. The last variable, Travel, is the target of the survey, the quantity of interest whose behaviour is under investigation.

## 统计代写|贝叶斯网络代写Bayesian network代考|Graphical Representation

The nature of the variables recorded in the survey, and more in general of the three categories they belong to, suggests how they may be related with each other. Some of these relationships will be direct, while others will be mediated by one or more variables (indirect).

Both kinds of relationships can be represented effectively and intuitively by means of a directed graph, which is one of the two fundamental entities characterising a BN. Each node in the graph corresponds to one of the variables in the survey. In fact, they are usually referred to interchangeably in the literature. Therefore, the graph produced from this example will contain six nodes, labelled after the variabless (A, S, E, $0, R$ and $T$ ). Direct dependence relationships are represented as arcs between pairs of variables (e.g., $A \rightarrow E$ means that $E$ depends on A). The node at the tail of the arc is called the parent, while that at the head (where the arrow is) is called the child. Indirect dependence relationships are not explicitly represented. However, they can be read from the graph as sequences of arcs leading from one variable to the other through one or more mediating variables (e.g., the combination of $A \rightarrow E$ and $E \rightarrow R$ means that $R$ depends on $A$ through $E$ ). Such sequences of arcs are said to form a path leading from one variable to the other; these two variables must be distinct. Paths of the form $\mathrm{A} \rightarrow \ldots \rightarrow \mathrm{A}$, which are known as cycles, are not allowed in the graph. For this reason, the graphs used in BNs are called directed acyclic graphs (DAGs).

Note, however, that some caution must be exercised in interpreting both direct and indirect dependencies. The presence of arrows or arcs seems to imply, at an intuitive level, that for each arc one variable should be interpreted as a cause and the other as an effect (e.g., $A \rightarrow E$ means that A causes $E$ ). This interpretation, which is called causal, is difficult to justify in most situations: for this reason, in general we speak about dependence relationships instead of causal effects. The assumptions required for causal BN modelling will be discussed in Section 6.7.

## 统计代写|贝叶斯网络代写Bayesian network代考| Train-Use Survey

• 性别（S）：生理性别，记为男性（M）或女性（F）。
• 教育（E）：成功完成的最高教育或培训水平，记录为高中（high）或大学学位（uni）。
• 职业（0）：个人是雇员（emp）还是个体经营者（self）。
• 居住地（R）：个人居住城市的大小，记为小（小）或大（大）。
• 旅行（T）：个人喜欢的交通工具，记为汽车（car）、火车（train）或其他（other）。
• 在本次调查的范围内，每个变量都属于三组之一。年龄和性别是人口统计指标。换句话说，它们是个体的内在特征；它们可能导致不同的行为模式，但不受个人本人的影响。另一方面，教育、职业和居住则相反。这些变量是社会经济指标，描述了个人在社会中的地位。因此，它们提供了个人预期生活方式的粗略描述；例如，它们可以描述他的消费习惯和工作日程。最后一个变量 Travel 是调查的目标，即正在调查其行为的兴趣数量。

## 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。