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

#### Doug I. Jones

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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
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## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Experiments, Outcomes, and Events

The act of tossing a coin and observing some outcome of interest, such as what side the coin lands on, can he regarded as an experiment. An example of an actual observation for the outcome of interest of this experiment would be “head.”

To avoid the confusion of different notions of outcome (as explained in the sidebar) we will only ever use the word outcome in the variable sense, that is, when we are talking about the outcome of interest of an experiment. Any actual observed value of an experiment will be referred to as an event, never an outcome. For example, in the experiment of rolling a die, where the outcome of interest is “the number showing on top” both “6” and “a number greater than 3 ” are events.

It is also important to distinguish between the notions of event and elementary event (see sidebar). Elementary events may also be called states.

In general there may be different outcomes of interest to us for the same experiment. For example, for coin tossing we might also be interested in the outcome “how long coin stays in the air” for which an actual observation might be ” $1.5$ seconds.” This is something we shall return to in Chapter 5 , but for the time being we will assume that there is a single clear outcome of interest for any given experiment.

All of the examples of uncertain events presented in the Introduction can be regarded as events arising from specific experiments with specific outcomes of interest. Box $4.2$ clarifies what the experiment, outcome of interest, and set of elementary events are in each case.

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

So far we have considered the outcome of a single experiment (also referred to as a trial). But we can consider not just the outcome of a single experiment but also the outcome of multiple repeated experiments (or trials).

For example, Figure $4.1$ shows all the possible elementary events arising from repeating the experiment of tossing a coin twice. In this tree diagram the edges are labeled by the possible elementary events from the single experiment. Each full path consists of two such edges and hence represents an elementary event of the repeated experiment. So, for example, the top-most path represents the elementary event where the first toss is a head $(\mathrm{H})$ and the second toss is a head (H). As shorthand we write the overall elementary event as $(\mathrm{H}, \mathrm{H})$ as shown in the last column. In this example there are nine possible elementary events.

We could do something similar for the bank experiment. Here we would consider successive days (Day 1, Day 2, etc.). On each day the set of possible elementary events are frauds only (F), lost transactions only (L), both frauds and lost transactions (B), and no loss (N). In this case the resulting multiple experiment results in outcomes like (F, $\mathrm{L}, \ldots),(\mathrm{F}, \mathrm{F}, \ldots),(\mathrm{N}, \mathrm{F}, \ldots)$, and so forth.

To calculate the number of possible elementary events of such repeated experiments we use the counting techniques described in Appendix A. If there are four elementary events of the single experiment, as in the bank case, then the number of elementary events of two experiments is equal to the number of samples of size two (with replacement) from four objects. This number is $4^{2}=16$ (see Appendix A). In general, if an experiment has $n$ elementary events and is repeated $r$ times, then the resulting multiple experiment has $n^{r}$ different elementary events. We call this enumeration. So

• Two successive throws of a die-Assuming the seven outcomes of a single throw, the answer is $7^{2}=49$.
• Five successive throws of a coin-Assuming again the three outcomes of a single throw, the answer is $3^{5}=243$.

# 贝叶斯分析代考

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

• 连续两次掷骰子-假设一次掷骰子有七个结果，答案是72=49.
• 五次连续投掷硬币-再次假设单次投掷的三个结果，答案是35=243.

## 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。

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