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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|贝叶斯分析代写Bayesian Analysis代考|Inconsistent Evidence

It is important to understand that sometimes evidence you enter in a $\mathrm{BN}$ will be impossible. For example, look at the NPT for the node People drown in Figure 7.28. If the node Flood is false then, no matter how good or bad the Quality of the emergency services, the state of the node People drown must be None because all other states have a probability zero in this case. There is, however, nothing to stop you entering the following two pieces of evidence in the $\mathrm{BN}$ :

• Flood is “false.”
• People drown is “1 to $5 . “$
If you attempt to run the model with these two observations you will (quite rightly) get a message telling you that you entered inconsistent evidence. What happens is that the underlying inference algorithm first takes one of the observations, say Flood is false and recomputes the other node probability values using Bayesian propagation. At this point the probability of People drown being 1 to 5 is calculated as zero. When the algorithm then tries to enter the observation People drown is “1 to 5 ” it therefore detects that this is impossible.

Entering inconsistent evidence will not always be as obvious as in the preceding example. One of the most common confusions when using $\mathrm{BNs}$ in practice occurs when entering evidence in large complex BNs. It is often the case that entering particular combinations of evidence will have an extensive ripple effect on nodes throughout the model. In some cases this will result in states of particular nodes having zero probability, in other words they are now impossible. These nodes might not be directly connected to the nodes where evidence was entered. If, in these circumstances, the user subsequently enters evidence that one of the impossible states is “true” the model, when computed, will produce an inconsistent evidence message that may surprise the user (who may user also has the tricky task of identifying which particular observation caused the inconsistent evidence.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Refuting the Assertion

One of the key lessons in Chapter 2 was that “correlation implies causation” is false. While this is widely known and accepted, many people do not realise that the converse implication
“Causation implies correlation”
is also false.
Indeed that, and the following equivalent assertions, are often wrongly assumed to be true:
“If there is no association (correlation) then there cannot be causation.”
“If there is causation there must be association (correlation).”
We can disprove these (equivalent) assertions with a simple counter-example using two Boolean variables $a$, and $b$, that is whose states are true or false. We do this by introducing a third, latent, unobserved Boolean variable $c$. Specifically, we define the relationship between $a, b$ and $c$ via the Bayesian network in Figure 7.46.

By definition $b$ is completely causally dependent on $a$. This is because, when $c$ is true the state of $b$ will be the same as the state of $a$, and when $c$ is false the state of $b$ will be the opposite of the state of $a$.

However, suppose – as in many real-world situations – that $c$ is both hidden and unobserved (i.e. a typical confounding variable as described in Chapter 2). Also, assume that the priors for the variables $a$ and $c$ are uniform (i.e. $50 \%$ of the time they are false and $50 \%$ of the time they are true).
Then when $a$ is false there is a $50 \%$ chance $b$ is false and a $50 \%$ chance $b$ is true. Similarly, when $a$ is true there is a $50 \%$ chance $b$ is false and a $50 \%$ chance $b$ is true. In other words, what we actually observe is zero association (correlation) despite the underlying mechanism being completely (causally) deterministic.

# 贝叶斯分析代考

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

• 洪水是“假的”。
• 淹死的人是“1到5.“
如果您尝试使用这两个观察结果运行模型，您将（非常正确地）收到一条消息，告诉您您输入了不一致的证据。发生的情况是，底层推理算法首先采用其中一个观察值，例如 Flood 为假，并使用贝叶斯传播重新计算其他节点的概率值。此时，人们溺水的概率为 1 到 5 被计算为零。然后，当算法尝试进入观察“淹死人数”为“1 到 5”时，它因此检测到这是不可能的。

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Refuting the Assertion

“因果关系意味着相关性”的相反含义

“如果没有关联（相关性），那么就不存在因果关系。”
“如果有因果关系，就必须有关联（相关性）。”

## 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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