## 统计代写|网络分析代写Network Analysis代考|CSE416a

statistics-lab™ 为您的留学生涯保驾护航 在代写网络分析Network Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写网络分析Network Analysis代写方面经验极为丰富，各种代写网络分析Network Analysis相关的作业也就用不着说。

• 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|网络分析代写Network Analysis代考|Rich club coefficient

The rich-club coefficient, introduced by Zhou and Mondragon in the context of the Internet topology [36], refers to the tendency of high-degree nodes (i.e., the hubs) in the network, to be very well-connected to other hub nodes. The name “rich-club” arises from the metaphor that the nodes with a large number of links, i.e., the hubs are “rich”, and they tend to be tightly and wellinterconnected between themselves, forming subgraphs called “club”. The rich-club coefficient is nothing but the measure of connectedness density within the club. A network with a rich club organization is shown in Fig. 4.4 for better understanding.

The nodes in a network can be categorized by a ranking scheme [36] or by their degree [8]. The rank $r$ of a node represents the corresponding position of the node in the list of descending order of node degrees, i.e., the most highly-connected node is ranked as $r=1$, the second best-connected node is $r=2$, and so on. The density of connections between the $r$ richest nodes is evaluated by the rich-club coefficient [36],
$$\Phi(r)=\frac{2 E(r)}{r(r-1)},$$
where $E(r)$ is the total number of links between $r$ hub nodes and $r(r-1) / 2$ is the maximum possible number of links among these nodes. Similarly, the rich-club coefficient [8] in terms of node de-gree can be represented as follows:
$$\Phi(k)=\frac{2 E_k}{N_k\left(N_k-1\right)},$$
where $E_k$ is the number of links present between the nodes of degree greater than or equal to $k$, and $N_k$ is the number of such nodes. Therefore, $\Phi(k)$ measures the fraction of actual links connecting those nodes and the maximum number of possible links. This measure explicitly reflects how densely connected are the nodes within a network.

The behavior of the rich-club coefficient is proportional to the value of $k$. It means, a rich-club coefficient increasing with the degree $k$ indicates that there exists a rich-club of nodes, which are densely interconnected than the nodes with smaller degrees. Contrarily, a decrease in the value of $\Phi(k)$ indicates the presence of many loosely connected and relatively independent subgroups. It is known as rich-club phenomenon.

## 统计代写|网络分析代写Network Analysis代考|Assortativity

Assortativity or assortative mixing was introduced by Newman [21]; is the tendency of nodes of a network (like social networks) to associate with others that are similar in some way. On the other hand, in nonsocial networks, such as biological networks, nodes with a high degree have a preference to associate with low-degree nodes. This tendency is referred as disassortative mixing, or disassortativity.

Assortativity is often quantified by the Pearson correlation between the excess degree distribution $q_k$ and the joint probability distribution $e_{j, k}[21]$. The excess degree is the number of edges leaving the node, other than the one that connects the pair. Similarly, the joint probability distribution is the distribution of the excess degrees of the two nodes at either end of a randomly chosen link. For an undirected graph, the assortativity is measured in terms of normalized Pearson coefficient of $e_{j, k}$ and $q_k$, and can be defined as
$$\rho=\frac{\sum_{j k} j k\left(e_{j k}-q_j q_k\right)}{\sigma_q^2}$$
where, $\delta$ is the standard deviation the of remaining degree distribution and $q_k$ is derived from the degree distribution $P_k$ as
$$q_k=\frac{(k+1) P_{k+1}}{\sum_{j \geq 1} j P_j}$$
In general, $\rho$ has a range from -1 to 1 , where 1 means a network has perfect assortativity, i.e., all nodes connect only with the nodes of a similar degree. If $\rho=0$, then the network has no assortativity, which means any node can randomly connect to any other node. Whereas, at $\rho=-1$, the network is completely disassortative; all nodes connect with the nodes of different degrees.

# 网络分析代考

## 统计代写|网络分析代写Network Analysis代考|Rich club coefficient

Zhou 和 Mondragon 在互联网拓扑的背景下引入的富倶乐部系数 [36]，指的是网络中高度节点（即中 心）与其他中心连接良好的趋势节点。“rich-club”这个名字来源于比喻具有大量链接的节点，即hubs是 “rich”，它们之间往往紧密且良好地相互联系，形成称为“club”的子图。富人倶乐部系数不过是衡量倶乐部 内部联系密度的指标。为了更好地理解，图 4.4 显示了具有丰富倶乐部组织的网络。

$$\Phi(r)=\frac{2 E(r)}{r(r-1)},$$

$$\Phi(k)=\frac{2 E_k}{N_k\left(N_k-1\right)},$$

## 统计代写|网络分析代写Network Analysis代考|Assortativity

Newman [21] 介绍了 Assortativity 或 assortative mixing；是网络节点（如社交网络) 与以某种方式相 似的其他节点关联的趋势。另一方面，在生物网络等非社交网络中，度数高的节点倾向于与度数低的节点 关联。这种趋势被称为异配混合或异配。

$$\rho=\frac{\sum_{j k} j k\left(e_{j k}-q_j q_k\right)}{\sigma_q^2}$$

$$q_k=\frac{(k+1) P_{k+1}}{\sum_{j \geq 1} j P_j}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|网络分析代写Network Analysis代考|MY561

statistics-lab™ 为您的留学生涯保驾护航 在代写网络分析Network Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写网络分析Network Analysis代写方面经验极为丰富，各种代写网络分析Network Analysis相关的作业也就用不着说。

• 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|网络分析代写Network Analysis代考|Clustering coefficient

Clustering coefficient $(\mathrm{cc})$ is a measure of affinity (likelihood), to which nodes in a network tends to create tightly connected group with each others. The tendency of likelihood of adjacent nodes in a network is higher in comparison to the nonadjacent nodes. There exists several alternatives [20], [10], [30] for defining clustering coefficient. Clemente et al. [5] generalized clustering coefficient measure for weighted and directed networks. Latapy et al. [19] and Opsahl [24] defined a new clustering coefficient measure for bipartite graph. However, among all, Watts and Strogatz [33] definitions of clustering coefficient is widely accepted. Furthermore, they introduced the concept of local and global, or network average clustering coefficient in their proposed approach. Local clustering coefficient $\left(\mathrm{CC}{v_i}\right)$ is the ratio of total number of edges that are present among the neighbors of a node $v_i$ to the total number of possible edges that could exist among the neighbors of $v_i$. Thus $\mathrm{CC}{v_i}$ for a directed graph is given as
$$C C_{v_i}=\frac{\sum_{j=1}^{\left|N_{v_i}\right|} \lambda\left(v_i, v_j\right)}{\left|N_{v_i}\right|\left(\left|N_{v_i}\right|-1\right)}$$
where, $\lambda\left(v_i, v_j\right)= \begin{cases}1, & \text { if }\left(v_i, v_j\right) \text { is connected, } \forall v_j \in N_{v_i}, i \neq j \ 0, & \text { otherwise. }\end{cases}$ $N_{v_i}=\left{v_k \mid e(i, k) \in \mathcal{E} \vee e(k, i) \in \mathcal{E}\right}$ is the set of adjacent nodes of $v_i$ in $\mathcal{V}$, and $\left|N_{v_i}\right|\left(\left|N_{v_j}\right|-1\right)$ is the total number of expected edges.
In the case of an undirected graph, the total number of expected edges will be $\frac{\left|N_{\varepsilon i}\right|\left(\left|N_{v_i}\right|-1\right)}{2}$, since $e(i, j)=e(j, i)$. Thus $C_{v_i}$ for an undirected graph can be represent as
$$c c_{v_i}=\frac{2 \times \sum_{j=1}^{\left|N_{v_i}\right|} \lambda\left(v_i, v_j\right)}{\left|N_{v_i}\right|\left(\left|N_{v_i}\right|-1\right)} .$$
The average (global) clustering coefficient [33] is the mean of $K$ local clustering coefficient. Therefore the global clustering coefficient for a graph $\mathcal{G}$ can be defined as
$$\overline{C C}=\frac{\sum_{i=1}^{\mathcal{V}} \mathrm{CC}_{v_i}}{\mathcal{V}}$$
where the range of $\overline{\mathrm{CC}}$ values lies within $0 \leq \overline{C C} \leq 1$.

## 统计代写|网络分析代写Network Analysis代考|Degree distribution

Degree distributions $\left(P_k\right)$ is the probability that a node chosen randomly has a degree $k$. Therefore, $P_k$ of a network is the fraction of nodes $(n)$ having degree $k\left(n_k\right)$. Assume a network with $n$ number of nodes and $n_k$ numbers of nodes having degree $k$, then, $P_k$ can be defined as follows:
$$P_k=\frac{n_k}{n}$$
For a large network with $\mathcal{V}$ nodes (where average degree $\langle k\rangle \ll$ $|\mathcal{V}|$ ), the degree distribution (4.8) approximately follows the Poisson distribution:
$$P_k=e^{-\langle k\rangle} \frac{\langle k\rangle^k}{k !}$$
Fig. 4.3 depicts the degree distribution of real-world networks, namely facebook, ca-GrQc, and ca-HepTh network. The degree distribution of real-world networks (like the Internet, social network, etc.) found to follow the power law (functional relationship) properties, which is defined as follows:
$$P_k \sim k^{-\gamma}$$
where $\gamma$ is a constant, and its value is bounded between 2 and 3.
Such a pattern is called a power law distribution, or a scalefree distribution, because the shape of the distribution does not change with scale (see Fig. 4.7).

# 网络分析代考

## 统计代写|网络分析代写Network Analysis代考|Clustering coefficient

$$C C_{v_i}=\frac{\sum_{j=1}^{\left|N_{v_i}\right|} \lambda\left(v_i, v_j\right)}{\left|N_{v_i}\right|\left(\left|N_{v_i}\right|-1\right)}$$

$$c c_{v_i}=\frac{2 \times \sum_{j=1}^{\left|N_{v_i}\right|} \lambda\left(v_i, v_j\right)}{\left|N_{v_i}\right|\left(\left|N_{v_i}\right|-1\right)} .$$

$$\overline{C C}=\frac{\sum_{i=1}^{\mathcal{V}} \mathrm{CC}_{v_i}}{\mathcal{V}}$$

## 统计代写|网络分析代写Network Analysis代考|Degree distribution

$$P_k=\frac{n_k}{n}$$

$$P_k=e^{-\langle k\rangle} \frac{\langle k\rangle^k}{k !}$$

$$P_k \sim k^{-\gamma}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|统计计算代写Statistical calculation代考|STA317

statistics-lab™ 为您的留学生涯保驾护航 在代写统计计算Statistical calculation方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写统计计算Statistical calculation代写方面经验极为丰富，各种代写统计计算Statistical calculation相关的作业也就用不着说。

• 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|统计计算代写Statistical calculation代考|Role of the computer in statistics

In all aspects of business life we are likely to encounter increasing quantities of data. Computers and new information technologies literally put data at our fingertips; for example, stock levels in a warehouse some distance away or share prices in Japan can be established in minutes.

The Internet can provide access to data across continents at low cost. The challenge is to organise and analyse this information in such a way that managers can make sense of it by utilising statistical and quantitative techniques. Facilities such as spreadsheets or statistical and mathematical software packages make analysis techniques readily available to everyone. The effective use of such computer software requires that you are able to interpret the output that can be generated, not only in a strictly quantitative way but also in assessing its potential to help in business decision-making.

Computers also provide the opportunity to experiment with and explore data in ways that would not otherwise be possible.

A computer may be efficiently used in any processing operation that has one or more of the following characteristics:

• large volume of input
• repetition of projects
• greater speed desired in processing
• greater accuracy
• processing complexities that require electronic help.
It can help you develop your ideas about how to organise the information by using a ‘try and refine’ approach, which can take too long to carry out manually.

## 统计代写|统计计算代写Statistical calculation代考|Sources of data: where to get the data

A statistical study may require the collection of new data from scratch, referred to as primary data, or be able to use already existing data, known as secondary data. It is also possible to use a combination of both sources.

Secondary data is already available in processed form, such as a database, the Internet, libraries or records kept within your company, and has been collected for some purpose other than you intend to use it for. Data is often collected through the use of secondary sources because it is available at low cost, but you need to be sure that you are not using unsuitable data just because it is easily available. Secondary data can be obtained internally or externally.

Internal data comes from within the organisation for its own use, for example from accounting records, payrolls, inventories, sales records, etc.

External data is collected from sources outside the organisation, such as trade publications, consumer price indexes, newspapers, libraries, universities, official statistics supplied by the Department of Statistics and other government departments, a Nielsen report on shopping behaviour, stock exchange reports. databases of the Department of Statistics, data on the unemployment rate supplied by the Department of Labour, or data on HIV/Aids provided by the Department of Health or websites on the Internet.

Primary data is information collected by those wishing to collect their own data. The distinguishing feature of this data is that it will be both reliable and relevant to your purpose. As a result, primary data can take a long time to collect and may be expensive. Sources of primary data include experiments, observation, group discussions and the use of questionnaires under controlled conditions.

There are multiple methods and tools that can be used to collect data, but you must decide which method(s) will best answer your research questions.
The four main methods of collecting data are:

• face to face
• by phone
• by post
• via the Internet.

# 统计计算代考

## 统计代写|统计计算代写Statistical calculation代考|Role of the computer in statistics

• 输入量大
• 重复项目
• 加工需要更快的速度
• 更高的准确性
• 处理需要电子帮助的复杂性。
它可以帮助您通过使用“尝试和完善”的方法来发展关于如何组织信息的想法，这可能需要很长时间才能手动执行。

• 面对面
• 用电话
• 通过邮寄
• 通过互联网。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|统计计算代写Statistical calculation代考|STAT407

statistics-lab™ 为您的留学生涯保驾护航 在代写统计计算Statistical calculation方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写统计计算Statistical calculation代写方面经验极为丰富，各种代写统计计算Statistical calculation相关的作业也就用不着说。

• 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|统计计算代写Statistical calculation代考|Problem-solving steps

Solving a statistical problem typically comprises the following steps:

1. Identify the problem and ask the question you hope to answer.
2. Collect the information (or data) needed to answer the problem: Identify an appropriate data source and decide how to measure it. Decide whether an existing data source is adequate or whether new data must be collected. Determine if you will use an entire population or a representative sample. If using a sample, decide on a viable sampling method.
3. Analyse the data: Organise and summarise the data into tables and graphs. which are effective ways to present data. Numerical summaries allow increased understanding by making use of single values to represent the data. This initial analysis provides insight into important characteristics of the data and gives guidance in selecting appropriate methods for further analysis.
4. Interpret the results in order to draw conclusions, make recommendations and assess the risk of an incorrect decision about the original problem under investigation. With sampling, the process usually involves generalising from a small group – or sample – of individuals or objects that were studied to a much larger group or population.

As part of a weekly quality check to access the calibration of a filling machine, the quality control manager randomly selects 50 bottles of beer that were filled on a specific day.

1. Ask a question: Is the calibration of the filling machine still within acceptable standards?
2. Collect the appropriate data: Randomly select 50 bottles on a specified day and measure the contents of each bottle. Record the measurements to the nearest millilitre.
3. Analyse the data: Summarise the data in a table and draw a graph, such as a scatter plot, to show the sample data as well as a line graph on the same plot to indicate the desired fill. The average fill of the sample bottles can also be calculated together with the standard deviation and other descriptive summary statistics.
4. Interpret the results and draw conclusions. For example: Compare the scatter plot with the required standard line graph to get a visual impression of any deviations. The sample average can also be compared with the required average to access the calibration of the filling machine. You can extend the results from the sample of 50 bottles to all bottles filled during that week.

## 统计代写|统计计算代写Statistical calculation代考|THE LANGUAGE OF STATISTICS

• An investigation or experiment is any process of observation or measurement.
• Elements are the people or objects about which information is collected.
• A population is the entire group about which you want information. If the population contains a countable number of items, it is said to be finite, and when the number of items is unlimited, it is said to be infinite. A study of the entire population is known as a census. A parameter is a numerical measure that describes the population. It is calculated using all the data of the population, such as an average. It is usually indicated by a letter from the Greek alphabet (e.g. $\mu, \sigma, \pi)$.
• To gain information about the population, a portion of the population data can be examined. This portion of data is called a sample. The sample must be representative of the population. A representative sample is one in which the relevant characteristics of the sample elements are generally the same as the characteristics of the population elements. A statistic is a numerical measure that describes a sample. It is usually indicated by a letter from the Roman alphabet (e.g. $x, s, n, p$ ).
• A variable is a characteristic of interest about each element of a population or sample. It is the topic about which data is collected, such as the age of first-year students at a university or the mass of each first-year student. Not all students are the same age or weigh the same; this will vary from student to student. That means there is a variation in the weights and ages. If there were no variability in the weights or ages, statistical inference would not be necessary. The observed values of the variable are the data you will use in a statistical investigation.
• Variables can be classified as quantitative or qualitative.
• Qualitative or categorical variables provide information that is nonnumerical, such as marital status, type of job, gender, etc. Qualitative information can sometimes be coded to make it appear quantitative, but will have no meaning on a number line.
• Quantitative variables provide numerical measurements of the elements of a study. Arithmetic operations such as addition and subtraction can be performed on the values of a quantitative variable.

# 统计计算代考

## 统计代写|统计计算代写Statistical calculation代考|Problem-solving steps

1. 确定问题并提出您希望回答的问题。
2. 收集回答问题所需的信息（或数据）：确定合适的数据源并决定如何衡量它。确定现有数据源是否足够或是否必须收集新数据。确定您将使用整个总体还是代表性样本。如果使用样本，请确定可行的抽样方法。
3. 分析数据：将数据组织和汇总为表格和图表。这是呈现数据的有效方式。数字摘要通过使用单个值来表示数据来增加理解。这种初步分析提供了对数据重要特征的深入了解，并为选择合适的方法进行进一步分析提供了指导。
4. 解释结果以得出结论、提出建议并评估对正在调查的原始问题做出错误决定的风险。通过抽样，这个过程通常涉及从一小群人或样本中将被研究的个体或对象推广到更大的群体或人口。

1. 问一个问题：灌装机的校准是否还在可接受的标准之内？
2. 收集适当的数据：在指定日期随机选择 50 个瓶子并测量每个瓶子的内容。记录测量值，精确到毫升。
3. 分析数据：汇总表格中的数据并绘制图表（例如散点图）以显示示例数据，并在同一图表上绘制折线图以指示所需的填充。样品瓶的平均填充量也可以与标准偏差和其他描述性汇总统计一起计算。
4. 解释结果并得出结论。例如：将散点图与所需的标准折线图进行比较，以获得任何偏差的视觉印象。样本平均值也可以与所需的平均值进行比较，以访问灌装机的校准。您可以将结果从 50 个瓶子的样本扩展到该周灌装的所有瓶子。

## 统计代写|统计计算代写Statistical calculation代考|THE LANGUAGE OF STATISTICS

• 调查或实验是任何观察或测量的过程。
• 元素是收集信息的人或物。
• 人口是您想要了解其信息的整个群体。如果总体包含可数的项目，则称它是有限的，而当项目的数量是无限的时，则称它是无限的。对整个人口的研究称为人口普查。参数是描述总体的数值度量。它是使用人口的所有数据（例如平均值）计算得出的。它通常由希腊字母表中的字母表示（例如米,p,π).
• 要获得有关人口的信息，可以检查人口数据的一部分。这部分数据称为样本。样本必须代表总体。代表性样本是样本要素的相关特征与总体要素的特征大致相同的样本。统计量是描述样本的数值度量。它通常由罗马字母表中的一个字母表示（例如X,秒,n,p ).
• 变量是关于总体或样本的每个元素的感兴趣特征。这是关于收集数据的主题，例如大学一年级学生的年龄或每个一年级学生的质量。并非所有学生的年龄或体重都相同；这将因学生而异。这意味着体重和年龄存在差异。如果体重或年龄没有变化，就没有必要进行统计推断。变量的观察值是您将在统计调查中使用的数据。
• 变量可以分为定量的或定性的。
• 定性或分类变量提供非数值信息，例如婚姻状况、工作类型、性别等。有时可以对定性信息进行编码以使其看起来是定量的，但在数轴上没有意义。
• 定量变量提供研究要素的数值测量。可以对定量变量的值执行加法和减法等算术运算。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|假设检验代写hypothesis testing代考|BSTA511

statistics-lab™ 为您的留学生涯保驾护航 在假设检验hypothesis testing作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在假设检验hypothesis testing代写方面经验极为丰富，各种假设检验hypothesis testing相关的作业也就用不着 说。

• 时间序列分析Time-Series Analysis
• 马尔科夫过程 Markov process
• 随机最优控制stochastic optimal control
• 粒子滤波 Particle Filter
• 采样理论 sampling theory

## 统计代写|假设检验代写hypothesis testing代考|Estimating the Standard Error of the Sample Quantile

Assuming that observations are randomly sampled from a continuous distribution, and that $f\left(x_q\right)>0$, the influence function of the qth quantile is
$$I F_q(x)= \begin{cases}\frac{q-1}{f\left(x_q\right)}, & \text { if } xx_q,\end{cases}$$
and
$$\hat{x}q=x_q+\frac{1}{n} \sum I F_q\left(X_i\right)$$ plus a remainder term that goes to zero as $n$ gets large. That is, the situation is similar to the trimmed mean in the sense that the estimate of the $q$ th quantile can be written as $x_q$, the population parameter being estimated, plus a sum of independent identically distributed random variables having a mean of zero, plus a term that can be ignored as the sample size gets large. Consequently, the influence function of the qth quantile can be used to determine the (asymptotic) standard error of $\hat{x}_q$. The result is $$V A R\left(\hat{x}_q\right)=\frac{q(1-q)}{n\left[f\left(x_q\right)\right]^2} .$$ For example, when estimating the median, $q=0.5$, and the variance of $\hat{x}{.5}$ is
$$\frac{1}{4 n\left[f\left(x_{.5}\right)\right]^2}$$
so the standard error of $\hat{x}{0.5}$ is $$\frac{1}{2 \sqrt{n} f\left(x{.5}\right)}$$
Moreover, for any $q$ between 0 and 1 ,
$$2 \sqrt{n} f\left(x_q\right)\left(\hat{x}_q-x_q\right)$$
approaches a standard normal distribution as $n$ goes to infinity.

## 统计代写|假设检验代写hypothesis testing代考|The Maritz–Jarrett Estimate of the Standard Error of x

Maritz and Jarrett (1978) derived an estimate of the standard error of sample median, which is easily extended to the more general case involving $\hat{x}_q$. That is, when using a single order statistic, its standard error can be estimated using the method outlined here. It is based on the fact that $E\left(\hat{x}_q\right)$ and $E\left(\hat{x}_q^2\right)$ can be related to a beta distribution. The beta probability density function, when $a$ and $b$ are positive integers, is
$$f(x)=\frac{(a+b+1) !}{a ! b !} x^a(1-x)^b, \quad 0 \leq x \leq 1 .$$
Details about the beta distribution are not important here. Interested readers can refer to Johnson and Kotz (1970, Chapter 24).

As before, let $m=[q n+0.5]$. Let $Y$ be a random variable having a beta distribution with $a=m-1$ and $b=n-m$, and let
$$W_i=P\left(\frac{i-1}{n} \leq Y \leq \frac{i}{n}\right) .$$
Many statistical computing packages have functions that evaluate the beta distribution, so evaluating the $W_i$ values is relatively easy to do. In $\mathrm{R}$, there is the function pbeta $(\mathrm{x}, \mathrm{a}, \mathrm{b})$ that computes $P(Y \leq x)$. Thus, $W_i$ can be computed by setting $x=i / n, y=(i-1) / n$, in which case $W_i$ is pbeta $(\mathrm{x}, \mathrm{m}-1, \mathrm{n}-\mathrm{m})$ minus pbeta $(\mathrm{y}, \mathrm{m}-1, \mathrm{n}-\mathrm{m})$.
Let
$$C_k=\sum_{i=1}^n W_i X_{(i)}^k$$
When $k=1, C_k$ is a linear combination of the order statistics. Linear sums of order statistics are called $L$-estimators. Other examples of L-estimators are the trimmed and Winsorized means already discussed. The point here is that $C_k$ can be shown to estimate $E\left(X_{(m)}^k\right)$, the $k$ th moment of the $m$ th order statistic. Consequently, the standard error of the $m$ th order statistic, $X_{(m)}=\hat{x}_q$, is estimated with
$$\sqrt{C_2-C_1^2}$$
Note that when $n$ is odd, this last equation provides an alternative to the McKean-Schrader estimate of the standard error of $M$ described in Section 3.3.4. Based on limited studies, it seems that when computing confidence intervals or testing hypotheses based on $M$, the McKean-Schrader estimator is preferable.

# 假设检验代写

## 统计代写|假设检验代写hypothesis testing代考|Estimating the Standard Error of the Sample Quantile

$$I F_q(x)=\left{\frac{q-1}{f\left(x_q\right)}, \quad \text { if } x x_q,\right.$$

$$\hat{x} q=x_q+\frac{1}{n} \sum I F_q\left(X_i\right)$$

$$\frac{1}{2 \sqrt{n} f(x .5)}$$

$$2 \sqrt{n} f\left(x_q\right)\left(\hat{x}_q-x_q\right)$$

## 统计代写|假设检验代写hypothesis testing代考|The Maritz–Jarrett Estimate of the Standard Error of x

Maritz 和Jarrett (1978) 得出了样本中位数标准误差的估计值，这很容易扩展到更一般的情况，涉及 $\hat{x}q$. 也就是说，当使用单阶统计量时，可以使用此处概述的方法估算其标准误差。这是基于这样一个事实 $E\left(\hat{x}_q\right)$ 和 $E\left(\hat{x}_q^2\right)$ 可能与 beta 分布有关。beta概率密度函数，当 $a$ 和 $b$ 是正整数，是 $$f(x)=\frac{(a+b+1) !}{a ! b !} x^a(1-x)^b, \quad 0 \leq x \leq 1$$ 关于 beta 分布的细节在这里并不重要。有兴趣的读者可以参考Johnson 和 Kotz（1970，第 24 章)。 和以前一样，让 $m=[q n+0.5]$. 让 $Y$ 是具有 beta 分布的随机变量 $a=m-1$ 和 $b=n-m$ ，然后让 $$W_i=P\left(\frac{i-1}{n} \leq Y \leq \frac{i}{n}\right) .$$ 许多统计计算包具有评估 beta 分布的函数，因此评估 $W_i$ 值是比较容易做到的。在 $\mathrm{R}$, 有函数 pbeta $(\mathrm{x}, \mathrm{a}, \mathrm{b})$ 计算 $P(Y \leq x)$. 因此， $W_i$ 可以通过设置计算 $x=i / n, y=(i-1) / n$ ，在这种情况下 $W_i$ 是 $\beta \beta(\mathrm{x}, \mathrm{m}-1, \mathrm{n}-\mathrm{m})$ 较少的 $\beta \beta(\mathrm{y}, \mathrm{m}-1, \mathrm{n}-\mathrm{m})$. 让 $$C_k=\sum{i=1}^n W_i X_{(i)}^k$$

$$\sqrt{C_2-C_1^2}$$

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国英国加拿大澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|假设检验代写hypothesis testing代考|STA2023

statistics-lab™ 为您的留学生涯保驾护航 在假设检验hypothesis testing作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在假设检验hypothesis testing代写方面经验极为丰富，各种假设检验hypothesis testing相关的作业也就用不着 说。

• 时间序列分析Time-Series Analysis
• 马尔科夫过程 Markov process
• 随机最优控制stochastic optimal control
• 粒子滤波 Particle Filter
• 采样理论 sampling theory

## 统计代写|假设检验代写hypothesis testing代考|The Finite Sample Breakdown Point

Before describing additional measures of location, it helps to introduce a technical device for judging any estimator that is being considered. This is the finite sample breakdown point of a statistic, which refers to the smallest proportion of observations that, when altered sufficiently, can render the statistic meaningless. More precisely, the finite sample breakdown point of an estimator refers to the smallest proportion of observations that when altered can cause the value of the statistic to be arbitrarily large or small. The finite sample breakdown point of an estimator is a measure of its resistance to contamination. For example, if the $i$ th observation among the observations $X_1, \ldots, X_n$ goes to infinity, the sample mean $\bar{X}$ goes to infinity as well. This means that the finite sample breakdown point of the sample mean is only $1 / n$. In contrast, the finite sample breakdown point of the $\gamma$-trimmed mean is $\gamma$. For example, if $\gamma=0.2$, about $20 \%$ of the observations can be made arbitrarily large without driving the sample trimmed mean to infinity, but it is possible to alter $21 \%$ of the observations so that $\bar{X}_t$ becomes arbitrarily large. Typically, the limiting value of the finite sample breakdown point is equal to the breakdown point, as defined in Chapter 2 , of the parameter being estimated. For example, the breakdown point of the population mean, $\mu$, is 0 , which equals $1 / n$ as $n$ goes to infinity. Similarly, the breakdown point of the trimmed mean is $\gamma$.

Two points should be stressed. First, having a high finite-sample breakdown point is certainly a step in the right direction when trying to deal with unusual values that have an inordinate influence, but it is no guarantee that an estimator will not be unduly influenced by even a small number of outliers. (Examples will be given when dealing with robust regression estimators.) Second, various refinements regarding the definition of a breakdown point have been proposed (e.g., Genton \& Lucas, 2003), but no details are given here.

## 统计代写|假设检验代写hypothesis testing代考|Estimating Quantiles

When comparing two or more groups, the most common strategy is to use a single measure of location, and the median or 0.5 quantile is an obvious choice. It can be highly advantageous to compare other quantiles as well, but the motivation for doing this is best explained in Chapter 5. For now, attention is focused on estimating quantiles and the associated standard error.

There are many ways of estimating quantiles, comparisons of which are reported by Parrish (1990), Sheather and Marron (1990), as well as Dielman, Lowry, and Pfaffenberger (1994). Here, two are described and their relative merits are discussed.
For any $q, 0<q<1$, let $x_q$ be the qth quantile. For a continuous random variable, or a distribution with no flat spots, $x_q$ is defined by the equation $P\left(X \leq x_q\right)=q$. This definition is satisfactory in the sense that there is only one value that qualifies as the qth quantile, so there is no ambiguity when referring to $x_q$. However, for discrete random variables or distributions with flat spots, special methods must be used to avoid having multiple values that qualify as the qth quantile. There are methods for accomplishing this goal, but they are not directly relevant to the topics of central interest in this book, at least based on current technology, so this issue is not discussed. ${ }^1$

Setting $m=[q n+0.5]$, where $[q n+0.5]$ is the greatest integer less than or equal to $q n+0.5$, the simplest estimate of $x_q$ is
$$\hat{x}q=X{(m)}$$
the mth observation after the data are put in ascending order. For example, if the goal is to estimate the median, then $q=1 / 2$, and if $n=11$, then $m=[11 / 2+0.5]=6$, and the estimate of $x_{.5}$ is the usual sample median, M. Of course, if $n$ is even, this estimator does not yield the usual sample median, it is equal to what is sometimes called the upper empirical cumulative distribution function estimator.

# 假设检验代写

## 统计代写|假设检验代写hypothesis testing代考|Estimating Quantiles

$$\hat{x} q=X(m)$$

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国英国加拿大澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|时间序列分析代写Time-Series Analysis代考|STAT3040

statistics-lab™ 为您的留学生涯保驾护航 在代写时间序列分析Time-Series Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写时间序列分析Time-Series Analysis代写方面经验极为丰富，各种代写时间序列分析Time-Series Analysis相关的作业也就用不着说。

• 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|时间序列分析代写Time-Series Analysis代考|Properties of ARMA Models

Pertaining to the stationarity, invertibility, and causality, the following theorem is not hard to understand.

Theorem 3.3 (1) The $\operatorname{ARMA}(p, q)$ is stationary if and only if its AR part is stationary. (2) The $\operatorname{ARMA}(p, q)$ is invertible if and only if its MA part is invertible.
(3) The $A R M A(p, q)$ is causal if and only if its AR part is causal.
For the coefficients $\left{\pi_j\right}$ in the $\operatorname{AR}(\infty)$ representation and the coefficients $\left{\psi_j\right}$ in the $\mathrm{MA}(\infty)$ representation, it is easy to prove the following propositions.

• If an $\operatorname{ARMA}(p, q)$ model defined by (3.7) is invertible, then its $\operatorname{AR}(\infty)$ representation is
$$\varepsilon_t=\sum_{j=0}^{\infty} \pi_j X_{t-j}=\left(\sum_{j=0}^{\infty} \pi_j B^j\right) X_t$$
where $\pi_0=1$ and for $j \geq 1$
$$\pi_j=-\sum_{k=1}^j \theta_k \pi_{j-k}-\varphi_j \text { where } \theta_k=0 \text { for } k>q, \varphi_j=0 \text { for } j>p .$$
• If an $\operatorname{ARMA}(p, q)$ model defined by (3.7) is causal, then its $\operatorname{MA}(\infty)$ representation is
$$X_t=\sum_{j=0}^{\infty} \psi_j \varepsilon_{t-j}=\left(\sum_{j=0}^{\infty} \psi_j B^j\right) \varepsilon_t$$
where $\psi_0=1$ and for $j \geq 1$
$$\psi_j=\sum_{k=1}^j \varphi_k \psi_{j-k}+\theta_j \text { where } \varphi_k=0 \text { for } k>p, \theta_j=0 \text { for } j>q .$$

## 统计代写|时间序列分析代写Time-Series Analysis代考|Model Building Problems

For building an ARMA model, a time series dataset is required to be stationary. Thus before estimating the ARMA model, we should check if the time series data is stationary using those procedures in Sect. 3.1.

In Chap. 3, we have given the definition of the ARMA model and elaborated on its properties. Now we know that Eq. (3.7) is the $\operatorname{ARMA}(p, q)$ model:
$$X_t=\varphi_0+\varphi_1 X_{t-1}+\cdots+\varphi_p X_{t-p}+\varepsilon_t+\theta_1 \varepsilon_{t-1}+\cdots+\theta_q \varepsilon_{t-q}$$
where $\left{\varepsilon_t\right} \sim \mathrm{WN}\left(0, \sigma_\epsilon^2\right), \varphi_p \neq 0, \theta_q \neq 0$ and $\varphi_0$ is the intercept (const). Another expression of the $\operatorname{ARMA}(p, q)$ model is
$$\varphi(B) X_t=\varphi_0+\theta(B) \varepsilon_t$$
where $\varphi(z)=1-\varphi_1 z-\cdots-\varphi_p z^p, \theta(z)=1+\theta_1 z+\cdots+\theta_q z^q$. Hence the number of parameters to be estimated is $p+q+2$. Additionally, in practice, $\operatorname{order}(p, q)$ is also unknown and needs to be determined.

There are two important procedures for selecting ARMA model order $(p, q)$. One is to firstly compute ACF as well as PACF and then by Table 3.1 to choose $\operatorname{order}(p, q)$. Another is a few information criteria such as AIC, BIC, HQIC, and so on. We will present these methods in detail in Sect. 4.3.

If $X_t$ has no seasonality and by differencing, we have that $Y_t=\nabla^d X_t=(1-$ $B)^d X_t$ is stationary (sometimes we need firstly transform the original series), then we can build an $\operatorname{ARMA}(p, q)$ model for $Y_t$ as follows:
$$\varphi(B) Y_t=\varphi_0+\theta(B) \varepsilon_t .$$
Expressing this model in terms of the original time series $X_t$, we have
$$\varphi(B)(1-B)^d X_t=\varphi_0+\theta(B) \varepsilon_t .$$

# 时间序列分析代考

## 统计代写|时间序列分析代写Time-Series Analysis代考|Properties of ARMA Models

(3) 的 $A R M A(p, q)$ 是因果关系当且仅当其 $\mathrm{AR}$ 部分是因果关系。 题。

• 如果 $\operatorname{ARMA}(p, q)(3.7)$ 定义的模型是可逆的，那么它的 $\mathrm{AR}(\infty)$ 代表是
$$\varepsilon_t=\sum_{j=0}^{\infty} \pi_j X_{t-j}=\left(\sum_{j=0}^{\infty} \pi_j B^j\right) X_t$$
在哪里 $\pi_0=1$ 并为 $j \geq 1$
$$\pi_j=-\sum_{k=1}^j \theta_k \pi_{j-k}-\varphi_j \text { where } \theta_k=0 \text { for } k>q, \varphi_j=0 \text { for } j>p .$$
• 如果 $\mathrm{ARMA}(p, q)$ 由 (3.7) 定义的模型是因果的，那么它的MA( $\mathrm{M})$ 代表是
$$X_t=\sum_{j=0}^{\infty} \psi_j \varepsilon_{t-j}=\left(\sum_{j=0}^{\infty} \psi_j B^j\right) \varepsilon_t$$
在哪里 $\psi_0=1$ 并为 $j \geq 1$
$$\psi_j=\sum_{k=1}^j \varphi_k \psi_{j-k}+\theta_j \text { where } \varphi_k=0 \text { for } k>p, \theta_j=0 \text { for } j>q$$

## 统计代写|时间序列分析代写Time-Series Analysis代考|Model Building Problems

$$X_t=\varphi_0+\varphi_1 X_{t-1}+\cdots+\varphi_p X_{t-p}+\varepsilon_t+\theta_1 \varepsilon_{t-1}+\cdots+\theta_q \varepsilon_{t-q}$$

$$\varphi(B) X_t=\varphi_0+\theta(B) \varepsilon_t$$

$$\varphi(B) Y_t=\varphi_0+\theta(B) \varepsilon_t$$

$$\varphi(B)(1-B)^d X_t=\varphi_0+\theta(B) \varepsilon_t$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|时间序列分析代写Time-Series Analysis代考|STAT758

statistics-lab™ 为您的留学生涯保驾护航 在代写时间序列分析Time-Series Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写时间序列分析Time-Series Analysis代写方面经验极为丰富，各种代写时间序列分析Time-Series Analysis相关的作业也就用不着说。

• 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|时间序列分析代写Time-Series Analysis代考|Stationarity and Causality of AR Models

Consider the AR(1) model:
$$X_t=\varphi X_{t-1}+\varepsilon_t, \varepsilon_t \sim \mathrm{WN}\left(0, \sigma_\epsilon^2\right)$$
For $|\varphi|<1$, let $X_{1 t}=\sum_{j=0}^{\infty} \varphi^j \varepsilon_{t-j}$ and for $|\varphi|>1$, let $X_{2 t}=-\sum_{j=1}^{\infty} \varphi^{-j} \varepsilon_{t+j}$. It is easy to show that both $\left{X_{1 t}\right}$ and $\left{X_{2 t}\right}$ are stationary and satisfy Eq. (3.6). That is, both are the stationary solution of Eq. (3.6). This gives rise to a question: which one of both is preferable? Obviously, $\left{X_{2 t}\right}$ depends on future values of unobservable $\left{\varepsilon_t\right}$, and so it is unnatural. Hence we take $\left{X_{1 t}\right}$ and abandon $\left{X_{2 t}\right}$. In other words, we require that the coefficient $\varphi$ in Eq. (3.6) is less 1 in absolute value. At this point, the AR(1) model is said to be causal and its causal expression is $X_t=\sum_{j=0}^{\infty} \varphi^j \varepsilon_{t-j}$. In general, the definition of causality is given below.

Definition 3.7 (1) A time series $\left{X_t\right}$ is causal if there exist coefficients $\psi_j$ such that
$$X_t=\sum_{j=0}^{\infty} \psi_j \varepsilon_{t-j}, \sum_{j=0}^{\infty}\left|\psi_j\right|<\infty$$
where $\psi_0=1,\left{\varepsilon_t\right} \sim \operatorname{WN}\left(0, \sigma_\epsilon^2\right)$. At this point, we say that the time series $\left{X_t\right}$ has an $\mathrm{MA}(\infty)$ representation. (2) We say that a model is causal if the time series generated by it is causal.

Causality suggests that the time series $\left{X_t\right}$ is caused by the white noise (or innovations) from the past up to time $t$. Besides, the time series $\left{X_{2 t}\right}$ is an example that is stationary but not causal. In order to determine whether an AR model is causal, similar to the invertibility for the MA model, we have the following theorem.

## 统计代写|时间序列分析代写Time-Series Analysis代考|Autoregressive Moving Average Models

Now we give the definition of ARMA models as follows.
Definition 3.8 (1) The following equation is called the autoregressive moving average model of order $(p, q)$ and denoted by $\operatorname{ARMA}(p, q)$ :
$$X_t=\varphi_0+\varphi_1 X_{t-1}+\cdots+\varphi_p X_{t-p}+\varepsilon_t+\theta_1 \varepsilon_{t-1}+\cdots+\theta_q \varepsilon_{t-q}$$
where $\left{\varepsilon_t\right} \sim \mathrm{WN}\left(0, \sigma_\epsilon^2\right), \mathrm{E}\left(X_s \varepsilon_t\right)=0$ if $s<t$, and $\left{\varphi_k\right}$ and $\left{\theta_k\right}$ are real-valued parameters (coefficients) with $\varphi_p \neq 0$ and $\theta_q \neq 0$. (2) If a time series $\left{X_t\right}$ is stationary and satisfies such an equation as (3.7), then we call it an $\operatorname{ARMA}(p, q)$ process.

We often assume the intercept (const term) $\varphi_0=0$. Using the backshift operator $B$, the $\operatorname{ARMA}(p, q)$ model can be rewritten as
$$\varphi(B) X_t=\theta(B) \varepsilon_t$$
where $\varphi(z)=1-\varphi_1 z-\cdots-\varphi_p z^p$ is the AR polynomial and $\theta(z)=1+\theta_1 z+$ $\cdots+\theta_q z^q$ is the MA polynomial. We always assume that $\varphi(z)$ and $\theta(z)$ have no common factors. Besides, $\varphi(B) X_t=\varepsilon_t$ and $X_t=\theta(B) \varepsilon_t$ are, respectively, called the $A R$ part and $M A$ part of the ARMA $(p, q)$ model. Of course, both the AR model and MA model are two special cases of the $\operatorname{ARMA}$ model: $\operatorname{AR}(p)=\operatorname{ARMA}(p, 0)$ and $\operatorname{MA}(q)=\operatorname{ARMA}(0, q)$

Example 3.11 (An ARMA(2,2) Model) Consider the following ARMA(2,2) model:
$$X_t=0.8 X_{t-1}-0.6 X_{t-2}+\varepsilon_t+0.7 \varepsilon_{t-1}+0.4 \varepsilon_{t-2}$$
We can simulate it with Python. Its time series plot is shown in Fig. 3.19 and looks stationary. In addition, its ACF and PACF plots are shown in Fig. 3.20. Both ACF and PACF seem to tail off, namely, for lag $k \geq 3$, and many ACF and PACF values are still nonzero. The Python code for this example is as follows.

# 时间序列分析代考

## 统计代写|时间序列分析代写Time-Series Analysis代考|Stationarity and Causality of AR Models

$$X_t=\varphi X_{t-1}+\varepsilon_t, \varepsilon_t \sim \mathrm{WN}\left(0, \sigma_\epsilon^2\right)$$

Veft $\left{X _{2 \text { t }} \backslash r i g h t\right}$. 换句话说，我们要求系数 $\varphi$ 在等式中 (3.6) 的绝对值小于 1。此时， $A R(1)$ 模型被称为 因果关系，其因果表达式为 $X_t=\sum_{j=0}^{\infty} \varphi^j \varepsilon_{t-j}$.一般来说，因果关系的定义如下。

$$X_t=\sum_{j=0}^{\infty} \psi_j \varepsilon_{t-j}, \sum_{j=0}^{\infty}\left|\psi_j\right|<\infty$$

## 统计代写|时间序列分析代写Time-Series Analysis代考|Autoregressive Moving Average Models

$$X_t=\varphi_0+\varphi_1 X_{t-1}+\cdots+\varphi_p X_{t-p}+\varepsilon_t+\theta_1 \varepsilon_{t-1}+\cdots+\theta_q \varepsilon_{t-q}$$

$$\varphi(B) X_t=\theta(B) \varepsilon_t$$

$\operatorname{AR}(p)=\operatorname{ARMA}(p, 0)$ 和 $\mathrm{MA}(q)=\operatorname{ARMA}(0, q)$

$$X_t=0.8 X_{t-1}-0.6 X_{t-2}+\varepsilon_t+0.7 \varepsilon_{t-1}+0.4 \varepsilon_{t-2}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

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

statistics-lab™ 为您的留学生涯保驾护航 在代写贝叶斯分析Bayesian Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写贝叶斯分析Bayesian Analysis代写方面经验极为丰富，各种代写贝叶斯分析Bayesian Analysis相关的作业也就用不着说。

• 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|Drug Testing

Here we dig deeper into the example (taken from Ziliak and McCloskey, 2008) first introduced in Chapter 2, Box 2.1. We are interested in comparing two weight-loss drugs to determine which should be sold. Experimental data on the drugs Oomph and Precision have shown that, over a one-month period for a number of test subjects:

• Weight loss for Precision is approximately Normally distributed with mean 5 pounds and variance 1 . So we define the NPT for the node Precision as a Normal $(5,1)$ distribution.
• Oomph showed a much higher average weight loss of 20 pounds but with much more variation and is estimated as a Normal $(20,100)$ distribution.
We might be interested in two things here: one is predictability of the effect of a drug on weight loss and the other is the size or impact of the drug on weight loss. Let’s adopt a similar formulation to before:
$$\begin{gathered} H_0: \text { Precision }>\text { Oomph } \ H_1: \text { Oomph } \geq \text { Precision } \end{gathered}$$
Figure 12.10 shows the AgenaRisk model used to test this hypothesis. Rather than create a node for the difference, Precision-Oomph, directly in AgenaRisk we have simply declared a single expression for the hypothesis node as
if (Precision > Oomph, “Precision”, “Oomph”)
rather than use two separate nodes as we did in the quality assurance example.

Notice that the hypothesis is approximately $93 \%$ in favor of Oomph over Precision, since only $7 \%$ of the time is Precision likely to result in more weight loss than Oomph. Interestingly we have included here two additional nodes to cover the risk that any of the drugs actually cause negative weight loss, that is, weight gain for the good reason that some may be fearful of putting on weight and might choose the drug that was less effective but also less risky. In this case someone might choose Precision since Oomph has a $2.28 \%$ chance of weight gain, where the chance of weight gain with Precision is negligible.
In the classical statistical approach to hypothesis testing in the drug testing example we would be interested in assessing the statistical significance of each drug with respect to its capability to reduce weight, that is, whether any weight reduction is likely to have occurred by chance. In doing this we compare the results for each drug against the null hypothesis: zero weight loss. So, for both Precision and Oomph we test the following hypotheses, where $\mu$ is the population mean weight loss in each case:
\begin{aligned} & H_0: \mu_0=0 \ & H_1: \mu_1>0 \end{aligned}
Box 12.2 describes the classical statistical approach to testing this hypothesis in each case (i.e. the approach introduced in Section 12.2.1).

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Considering Difference between Distributions Rather Than Difference between Means

Consider the following problem scenario:
A new drug is trialled which is believed to increase survival time of patients with a particular disease. It is a comprehensive randomised control trial lasting 36 months in which 1000 patients with the disease take the drug and 1000 with the disease do not take the drug. The trial results show that the null hypothesis of “no increase in survival time” can be rejected with high confidence; specifically, there is greater than $99 \%$ chance that the mean survival time of people taking the drug is higher than those who do not. You are diagnosed with the disease. Should you take the drug and, if so, what are your chances of surviving longer if you do?
As in the previous problems we are comparing two attributes-the survival time with the drug and the survival time without the drug. Unfortunately, the $99 \%$ probability that the mean of the former is greater than the mean of the latter tells us nothing about the probability that any given person will survive longer if they take the drug. So, it does not help us to answer the question. The problem is that if we have reasonable size samples-as in this case-there will actually be very little uncertainty about the mean. All the “interesting” uncertainty is about the variance. As an extreme example suppose you could measure the height of every adult male in the United Kingdom. Then, despite wide variance in the results, the mean height will be an exact figure, say $176 \mathrm{~cm}$. Even if you were only able to take a sample of, say 100 , the mean of the sample would be a very accurate estimate of the true mean of 176 (i.e. with very little uncertainty). So, in the drug example, if the mean survival time of the 1000 patients taking the drug is 28.5 weeks, then this will be very close to the true, but unknown, survival time with little uncertainty. Yet the mean survival time will inevitably “hide” the fact that many of the patients survive the full 36 weeks while many die within the first 3 weeks.

Suppose that, based on the trial data, we get the following estimates for the mean and variance of the survival times:

Then we can construct the necessary $\mathrm{BN}$ model as shown in Figure 12.11.

The nodes with the estimated means and variances of the survival times are defined using the Normal distributions in the above table. Each of the “true” survival time nodes is defined simply as a Normal distribution with mean equal to the (parent) estimated mean and variance equal to the (parent) estimated variance. The Boolean node “Mean survival time no greater with drug” has its NPT defined as
if(mean_with > mean_without, ‘False’, ‘True’)
The Boolean node “survive no longer with drug” has its NPT defined as
if(with > without, ‘False’, ‘True’)
Note that the null hypothesis “Mean survival time no greater with drug” is easily rejected at the $1 \%$ level, and so the drug would certainly be accepted and recommended for patients with the disease. However, the situation for the null hypothesis “survive no longer with drug” is very different. There is actually a $47.45 \%$ chance that your survival time will be less if you take the drug than if you do not.

# 贝叶斯分析代考

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

• Precision 的体重减轻近似正态分布，均值为 5 磅，方差为 1 。所以我们将节点 Precision 的 NPT 定义为 $\operatorname{Normal}(5,1)$ 分配。
• Oomph 表现出更高的平均体重减轻 20 磅，但变化更大，估计为正常 $(20,100)$ 分配。 我们可能对这里的两件事感兴趣：一是药物对减肥效果的可预测性，二是药物对减肥的大小或影 响。让我们采用与之前类似的公式:
$$H_0: \text { Precision }>\text { Oomph } H_1: \text { Oomph } \geq \text { Precision }$$
图 12.10 显示了用于检验该假设的 AgenaRisk 模型。我们没有直接在 AgenaRisk 中为差值 Precision-Oomph 创建一个节点，而是简单地为假设节点声明了一个表达式，就像 (Precision > Oomph, “Precision”, “Oomph”) 而不是像我们一样使用两个单独的节点在质量保证示例中做了。
请注意，假设大约是 $93 \%$ 赞成 Oomph 而不是 Precision，因为只有 $7 \%$ 与 Oomph 相比，Precision 可 能会导致更多的体重减轻。有趣的是，我们在这里包括了两个额外的节点，以涵盖任何药物实际导致负 体重减轻的风险，即体重增加的充分理由是一些人可能害怕增加体重并可能选择效果较差的药物而且风 险也较小。在这种情况下，有人可能会选择 Precision，因为 Oomph 有 $2.28 \%$ 体重增加的机会，其中 Precision 增加体重的机会可以忽略不计。
在药物测试示例中假设检验的经典统计方法中，我们有兴趣评估每种药物在其减肥能力方面的统计显着 性，即任何体重减轻是否可能是偶然发生的。在这样做时，我们将每种药物的结果与零假设进行比较: 体重减轻为零。因此，对于 Precision 和 Oomph，我们检验以下假设，其中 $\mu$ 是每种情况下的总体平均 体重减轻:
$$H_0: \mu_0=0 \quad H_1: \mu_1>0$$
专栏 12.2 描述了在每种情况下检验该假设的经典统计方法 (即第 12.2 .1 节中介绍的方法)。

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Considering Difference between Distributions Rather Than Difference between Means

if(mean_with > mean_without, ‘False’, ‘True’)

if(with > without, ‘False’, ‘True’)

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|MAST90125

statistics-lab™ 为您的留学生涯保驾护航 在代写贝叶斯分析Bayesian Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写贝叶斯分析Bayesian Analysis代写方面经验极为丰富，各种代写贝叶斯分析Bayesian Analysis相关的作业也就用不着说。

• 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 Bayesian Approach Avoids p-Values Completely

What we really want to do is determine the probability that the null hypothesis is true given the data observed. This is precisely what the Bayesian approach provides. Moreover it enables us to:

• Achieve a completely rational and unifying approach to hypothesis testing.
• Avoid all ambiguity about the meaning of the null and alternative hypothesis, including what assumptions are being made about them.
• Expose potential flaws in the classical approach.
• Identify precisely what assumptions in the classical case are needed for it to “make sense.”
The generic BN for the coin tossing hypothesis problem (which will enable us to capture every possible type of assumption and also extends to arbitrary number of coin tosses) is shown in Figure 12.3.

The Boolean nodes $H$ and ” $p H>0.5$ ?” – which would not normally be made explicit in a $\mathrm{BN}$ of this kind-are included since these are the nodes that clarify the assumptions being made in the different approaches. In a Bayesian approach we are allowed to condition the prior for the unknown $\mathrm{pH}$ on our background knowledge. Moreover, as we shall see, this is the (only) way of capturing exactly what we mean by a biased/non-biased coin. In the Bayesian approach we are also, of course, allowed to incorporate any prior knowledge about whether or not the coin is biased or not (although in most of what follows we will assume this is $50: 50$ ).

All of the key differences and assumptions are captured in the way we define the prior probability of node $\mathrm{pH}$ given the hypothesis. We consider some different possible assumptions in the following cases.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Testing for Hypothetical Differences

The hypothesis concerns the probability of faultiness for each material, $p_A$ and $p_B$, respectively:
\begin{aligned} & H_0: p_A \geq p_B \ & H_1: p_A<p_B \end{aligned}
Let’s assume that the testing yielded 10 faults in 200 samples of material A and 15 faults in 200 samples of material B.

Before producing a solution here we first need to make an assumption about the prior probability of the materials being faulty. It seems reasonable to be indifferent here and select an ignorant prior where all probabilities of faultiness are equally likely. So we choose the Uniform $(0,1)$ distribution as the prior distribution for both $p_A$ and $p_B$. As we explained in Chapter 6 , the Binomial $(n, p)$ distribution (with $n$ equal to the number of samples and $p$ equal to the probability of faultiness) is a reasonable choice for modeling the likelihood of observing a number of faults in a sample of size $n$. We can use this for both material A and material B.
We can represent all of this information in a Bayesian network:

• Clearly we need nodes $p_A$ and $p_B$ to represent the probability of faultiness for each of the materials (the node probability tables [NPTs] for these nodes will be the $\mathrm{U}(0,1)$ distribution).
• We clearly also need nodes to represent the number of faults in the respective samples (the NPTs for these nodes will be the Binomial distributions).
All that remains is to specify the nodes associated with our hypothesis. This is easily done by recasting the hypotheses as a difference, since $p_A \geq p_B$ is equivalent to $p_A-p_B \geq 0$ :
\begin{aligned} & H_0: p_A-p_B \geq 0 \ & H_1: p_A-p_B<0 \end{aligned}
We therefore need to add an additional node to represent the function $\left(p_A-p_B\right)$ with parent nodes $p_A$ and $p_B$, and a Boolean child node of $\left(p_A-p_B\right)$ to represent the hypothesis itself.

The resulting BN is shown in Figure 12.8 with the prior distribution for the hypothesis node displayed. As you can see the hypothesis is 50:50 for $H_0: H_1$.

We can now enter the testing data into the $\mathrm{BN}$ as evidence (shown in Figure 12.9) and can see that the distributions for $p_A, p_B$ and $\left(p_A-p_B\right)$ have all been updated and that the percentage probability that material $\mathrm{A}$ is better than material B is $84 \%$.

# 贝叶斯分析代考

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|The Bayesian Approach Avoids p-Values Completely

• 实现一种完全理性和统一的假设检验方法。
• 避免所有关于原假设和备择假设含义的歧义，包括对它们所做的假设。
• 暴露经典方法中的潜在缺陷。
• 准确确定经典案例中需要哪些假设才能使其“有意义”。
图 12.3 显示了抛硬币假设问题的通用 BN (这将使我们能够捕获每一种可能的假设类型，并且还 可以扩展到任意数量的抛硬币)。
布尔节点 $H$ 和” $p H>0.5$ ? – 通常不会在 $\mathrm{BN}$ 包括这种类型的节点，因为这些节点阐明了不同方法中所 做的假设。在贝叶斯方法中，我们可以为末知条件设定先验条件 $\mathrm{pH}$ 关于我们的背景知识。此外，正如我 们将看到的，这是 (唯一) 准确捕捉我们所说的有偏见/无偏见硬币的意思的方法。当然，在贝叶斯方法 中，我们也可以结合任何关于硬币是否有偏差的先验知识（尽管在接下来的大部分内容中我们会假设这 是 $50: 50)$.
我们定义节点先验概率的方式捕获了所有关键差异和假设 $\mathrm{pH}$ 给定假设。我们在以下情况下考虑一些不同 的可能假设。

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Testing for Hypothetical Differences

$$H_0: p_A \geq p_B \quad H_1: p_A<p_B$$

• 显然我们需要节点 $p_A$ 和 $p_B$ 表示每种材料的故障概率（这些节点的节点概率表 [NPTs] 将是U $\mathrm{U}(0,1)$ 分配）。
• 我们显然还需要节点来表示各个样本中的故障数量（这些节点的 NPT 将是二项分布）。 剩下的就是指定与我们的假设相关的节点。这很容易通过将假设重铸为差异来完成，因为 $p_A \geq p_B$ 相当于 $p_A-p_B \geq 0$ :
$$H_0: p_A-p_B \geq 0 \quad H_1: p_A-p_B<0$$
因此，我们需要添加一个额外的节点来表示函数 $\left(p_A-p_B\right)$ 与父节点 $p_A$ 和 $p_B$ ，和一个布尔子节点 $\left(p_A-p_B\right)$ 代表假设本身。
生成的 BN 如图 12.8 所示，其中显示了假设节点的先验分布。如您所见，假设是 50:50 $H_0: H_1$.
我们现在可以将测试数据输入到 $\mathrm{BN}$ 作为证据（如图 12.9 所示)，可以看出 $p_A, p_B$ 和 $\left(p_A-p_B\right)$ 已经 全部更新，并且该材料的百分比概率 $\mathrm{A}$ 比材料 $\mathrm{B}$ 好 $84 \%$.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。