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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|概率与统计作业代写Probability and Statistics代考|Sampling Plans and Estimates

In the previous chapter we computed descriptive statistics for the dataset on faces. The results showed that the average rating was $58.37$ and that men rated the faces higher than women on average. If we are only interested in the participants in the study and we are willing to believe that the results are fully deterministic, ${ }^1$ we could claim that the group of men rates higher than the group of women on average. However, if we believe that the ratings are not constant for one person for the same set of faces ${ }^2$ or if we would like to know whether our statements would also hold for a larger group of people (who did not participate in our experiment), we must understand what other results could have been observed in our study if we had conducted the experiment at another time with the same group of participants or with another group of participants.

To be able to extend your conclusions beyond the observed data, which is called more technically statistical inference, you should wonder where the dataset came from, how participants were collected, and how the results were obtained. For example, if the women who participated in the study of rating faces all came from one small village in the Netherlands, while the men came from many different villages and cities in the Netherlands, you would probably agree that the comparison between the average ratings from men and women becomes less meaningful. In this situation the dataset is considered selective towards women in the small village. Selective means here that not all women from the villages and cities included in the study are represented by the women in the study, but only a specific subgroup of women have been included. To overcome these types of issues, we need to know about the concepts of population, sample, sampling procedures, and estimation of population characteristics, and also how these concepts are related to each other to be able to do proper statistical inference.

Figure $2.1$ visualizes the relation between these concepts. On the left side we have a population of units (e.g., all men and women from the Netherlands) and on the right side we have a subset of units (the sample). Sampling procedures are formal probabilistic approaches to help collect units from the population for the sample. For the sample we like to use $x_1, x_2, \ldots, x_n$ for the observations of a certain variable (e.g., ratings on faces from pictures). The calculations on the sample data, which we have learned in Chap. 1, are ways of describing the sample. For the population the same notation $x_1, x_2, \ldots, x_N$ for all $N$ units is used. Here we have used the same indices for the sample and the population, but this does not mean that the sample $x_1$, $x_2, \ldots, x_n$ is just the first $n$ units from the population $x_1, x_2, \ldots, x_N$. Mathematically. we should have written $x_{i_1}, x_{i_2}, \ldots, x_{i_n}$ for the sample data, with $i_h \in{1,2, \ldots, N}$ and $i_h \neq i_l$ when $h \neq l$, since any set of units $i_1, i_2, \ldots, i_n$ from the population could have ended up in the sample. The values in the sample are referred to as a realization from the population.

## 统计代写|概率与统计作业代写Probability and Statistics代考|Definitions and Standard Terminology

In this section we briefly introduce some definitions and standard terminology. Frequently, we wish to say something about a group of units other than just the ones we have measured. A unit is usually a concrete or physical thing for which we would like to measure its characteristics. In medical research and the social sciences units are mostly human beings, while in industry units are often products, but units can essentially be anything: text messages, financial transitions, sales, etc. The complete set of units that we would like to say something about is called the (target) population. The set of units for which we have obtained data is referred to as the sample. The sample is typically a subset of the population, although in theory the sample can form the whole population or the sample can contain units that are not from the target population. If we are interested in individuals in the age range of 25 years to 65 years, it could happen that a person with an age outside this range is accidently included in the sample.

Statistics is concerned with how we can say things, and what we can say, about a population given that we have only observed our sample data. As we mentioned before, we call this statistical inference: “Statistical inference is the process of deducing properties of an underlying population by analysis of the sample data. Statistical inference includes testing hypotheses for the population and deriving population estimates.”, see e.g., Casella and Berger (2002).

In many situations it is unnecessary to specify the unit explicitly since it will be clear from the context, but it is not always easy to determine the unit. For instance,a circuit board contains many different components. Testing the quality of a circuit board after it has been produced requires the testing of all or a subset of the components. In this case it is not immediately clear whether the circuit board itself or whether the components are the units. In this setting the circuit board is sometimes referred to as the sample unit, since it is the unit that is physically taken from the production process. The components on the circuit board are referred to as observation units, since it is the unit that is measured. If the components were to be tested before being placed on the circuit board, however, the component would represent both the sample and observation unit. ${ }^4$

# 概率与统计作业代考

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## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师