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# 统计代写|统计推断代考Statistical Inference代写|Venn Mnemonic for the Rules of Probability

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## 统计代写|统计推断代考Statistical Inference代写|Venn Mnemonic for the Rules of Probability

It is often useful to have a picture to represent the mathematics, so that it is easier to remember the equations and to understand their meaning. It is common to use what is called a Venn Diagram to represent probabilities in an intuitive, graphical way. The idea is that probabilities are represented as the fractional area of simple geometric shapes. We can then find a picture representation of each of the rules of probability. We start by looking at a sample Venn Diagram, in Figure 1.2.

The fractional area of the rectangle $A$ represents the probability $P(A)$, and can be thought of as a probability of one of the statements we’ve explored, such as $P(\Downarrow)$. This diagram is strictly a mnemonic, because the individual points on the diagram are not properly defined. The diagram in Figure 1.2 also represents the Negation Rule (Equation 1.7),
$$P(A)+P(\operatorname{not} A)=1$$
In the diagram it is easy to see that the sum of the areas inside of $A$ (i.e. 1/4) and outside of $A$ (i.e. 3/4) cover the entire area of the Universe of statements, and thus add up to 1.

Figure 1.3 shows the diagram which can help us remember the sum and product rules. The Sum Rule (Equation 1.10)
$$P(A \text { or } B)=P(A)+P(B)-P(A \text { and } B)$$
is represented in the total area occupied by the rectangles $A$ and $B$, and makes up all of $A$ (i.e. $1 / 4$ ) and the half of $B$ sticking out (i.e. $1 / 8-1 / 16=1 / 16)$ yielding $P(A$ or $B)=5 / 16$. This is also the area of each added up $(1 / 4+1 / 8)$, but subtracting the intersection $(1 / 16)$ because otherwise it is counted twice. Adding the areas this way directly parallels the Sum Rule.

## 统计代写|统计推断代考Statistical Inference代写|Lessons from Bayes’ Rule – A First Look

Bayes’ Rule is the gold standard for all statistical inference. It is a mathematical theorem, proven from fundamental principles. It structures all inference in a systematic fashion. However, it can be used without doing any calculations, as a guide to qualitative inference. Some of the lessons which are consequences of Bayes’ Rule are listed here, and will be noted throughout this text in various examples.

• Confidence in a claim should scale with the evidence for that claim
• Ockham’s razor, which is the philosophical idea that simpler theories are preferred, is a consequence of Bayes’ Rule when comparing models of differing complexity.
• Simpler means fewer adjustable parameters
• Simpler also means that the predictions are both specific and not overly plastic. For example, a hypothesis which is consistent with the observed data, and also be consistent if the data were the opposite would be overly plastic.
• Your inference is only as good as the hypotheses (i.e. models) that you consider.
• Extraordinary claims require extraordinary evidence. ${ }^7$
• It is better to explicitly display your assumptions rather than implicitly hold them.
• It is a good thing to update your beliefs when you receive new information.
• Not all uncertainties are the same.

# 统计推断代写

## 统计代写|统计推断代考Statistical Inference代写|Venn Mnemonic for the Rules of Probability

$$P(A)+P(\operatorname{not} A)=1$$

$$P(A \text { or } B)=P(A)+P(B)-P(A \text { and } B)$$

## 统计代写|统计推断代考Statistical Inference代写|Lessons from Bayes’ Rule – A First Look

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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。