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

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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

Table $2.1$ contains the (annualized) growth rate figures for the UK for each quarter from the start of 1993 to the end of 2007 (which was just prior to the start of the international economic collapse). So, for example, in the fourth quarter of 2007 the annual growth rate in the UK was $2.36 \%$.

Data such as this, especially given the length of time over which it has been collected, is considered extremely valuable for financial analysis and projections. Since so many aspects of the economy depend on the growth rate, we need our predictions of it for the coming months and years to be very accurate. So imagine that you were a financial analyst presented with this data in 2008 . Although it would be nice to be able to predict the growth rate in each of the next few years, the data alone gives you little indication of how to do that. If you plot the growth over time as in Figure $2.1$ there is no obvious trend to spot.

But there is a lot that you can do other than making “point” predictions. What financial institutions would really like to know is the answer to questions like those in Sidebar 2.1.

Indeed, economic analysts feel that the kind of data provided enables them to answer such questions very confidently. The way they typically proceed is to “fit” the data to a standard curve (also called a statistical distribution). The answers to all the aforementioned questions can then be answered using standard statistical tables associated with that distribution.

统计代写|贝叶斯分析代写Bayesian Analysis代考|Risk Assessment and Decision Analysis with Bayesian Networks

In most cases the analysts assume that data of the kind seen here can be fitted by what is called a Normal distribution (also called a bell curve because that is its shape as shown in Figure 2.2).

The key thing about a Normal distribution is that it is an “idealized” view of a set of data. Imagine that, instead of trying to model annual growth rate, you were trying to model the height in centimeters of adults. Then, if you took a sample of, say, 1,000 adults and plotted the frequency of their heights within each 10 -centimeter interval you would get a graph that looks something like Figure 2.3. As you increase the sample size and decrease the interval size you would eventually expect to get something that looks like the Normal distribution in Figure 2.4.

The Normal distribution has some very nice mathematical properties (see Box 2.1), which makes it very easy for statisticians to draw inferences about the population that it is supposed to be modelling.

Unfortunately, it turns out that, for all its nice properties the Normal distribution is often a very poor model to use for most types of risk assessment. And we will demonstrate this by returning to our GDP growth rate data. In the period from 1993 to 2008 the average growth rate was $2.96 \%$ with a standard deviation of $0.75$.

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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。