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# 统计代写|贝叶斯统计代写Bayesian Statistics代考|CHS717 Radio control towers

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In a hypothetical war, two radio control workers, Mr Pearson (from the county of Frequentland) and Mr Laplace (from the county of Bayesdom), sit side by side and are tasked with finding an enemy plane that has been spotted over the country’s borders. They will each feed this information to the nearest air force base(s), which will respond by sending up planes of their own. There are, however, two different air forces – one for each county. Although the air forces of Frequentland and Bayesdom share airbases, they are distinct, and only respond to Mr Pearson’s and Mr Laplace’s advice, respectively. The ongoing war, though short, has been costly to both allies, and they each want to avoid needless expenditure while still defending their territory.
Mr Pearson starts by inputting the plane’s radar information into a computer program that uses a model of a plane’s position which has been calibrated against historical enemy plane data. The result comes out instantly:
The plane is most likely 5 miles North of the town of Tunbridge Wells.
Without another moment’s thought, Mr Pearson radios the base of Tunbridge Wells, telling them to scramble all 10 available Frequentist fighter jets immediately. He then gets up and makes himself a well-earned coffee.

Mr Laplace knows from experience that the enemy has used three different flight paths to attack in the past. Accordingly, he gives these regions a high probability density in his prior for the plane’s current location and feeds this into the same computer program used by Mr Pearson. The output this time is different. By using the optional input, the program now outputs a map with the most likely regions indicated, rather than a single location. The highest posterior density is over the region near Tunbridge Wells, where Mr Pearson radioed, although the map suggests there are two other towns which might also be victims of the plane’s bombing. Accordingly, Mr Laplace radios to Tunbridge Wells, asking them to send up four jets, and to the other two towns, asking them to send up two jets each. At the end of all this, Mr Laplace remains seated, tired but contented that he has done his best for his own.

The enemy bomber turned out to be approaching Berkstad, one of the towns which Mr Laplace radioed. The Bayesdom jets intercept the encroaching plane and escort it out of allied airspace. Mr Laplace is awarded a medal in honour of his efforts. Pearson looks on jealously.

## 统计代写|贝叶斯统计代写Bayesian Statistics代考|BAYESIAN INFERENCE VIA BAYES’ RULE

Bayes’ rule tells us how to update our prior beliefs in order to derive better, more informed, beliefs about a situation in light of new data. In Bayesian inference, we test hypotheses about the real world using these posterior beliefs. As part of this process, we estimate characteristics that interest us, which we call parameters, that are then used to test such hypotheses. From this point onwards we will use $\theta$ to represent the unknown parameter(s) which we want to estimate.

The Bayesian inference process uses Bayes’ rule to estimate a probability distribution for those unknown parameters after we observe the data. (Don’t worry if you don’t know what is meant by a probability distribution since we shall devote the entirety of Chapter 3 to this purpose.) However, it is sufficient for now to think of probability distributions as a way to represent uncertainty for unknown quantities.
Bayes’ rule as used in statistical inference is of the form:
$$p(\theta \mid \text { data })=\frac{p(\text { data } \mid \theta) \times p(\theta)}{p(\text { data })},$$
where we use $p$ to indicate a probability distribution which may represent either probabilities or, more usually, probability densities (see Section 3.3.2 for a description of their distinction). We shall now spend the next few sections describing, in short, the various elements of expression (2.5). This will only be a partial introduction since we spend the entirety of Part II on an extensive discussion of each of the constituent components.

## 统计代写|贝叶斯统计代写Bayesian Statistics代考|BAYESIAN INFERENCE VIA BAYES’ RULE

$$p(\theta \mid \text { data })=\frac{p(\text { data } \mid \theta) \times p(\theta)}{p(\text { data })}$$

## 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。