### 统计代写|统计推断作业代写statistical inference代考|Conditional probability, motivation

statistics-lab™ 为您的留学生涯保驾护航 在代写 统计推断statistical inference方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写统计推断statistical inference方面经验极为丰富，各种代写 统计推断statistical inference相关的作业也就用不着说。

• 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

## 统计代写|统计推断作业代写statistical inference代考|Conditional probability, motivation

Conditioning a central subject in statistics. If we are given information about a random variable, it changes the probabilities associated with it. For example, the probability of getting a one when rolling a (standard) die is usually assumed to be one sixth. If you were given the extra information that the die roll was an odd number (hence 1,3 or 5 ) then conditional on this new information, the probability of a one is now one third.

This is the idea of conditioning, taking away the randomness that we know to have occurred. Consider another example, such as the result of a diagnostic imaging test for lung cancer. What’s the probability that a person has cancer given a positive test? How does that probability change under the knowledge that a patient has been a lifetime heavy smoker and both of their parents had lung cancer? Conditional on this new information, the probability has increased dramatically.

## 统计代写|统计推断作业代写statistical inference代考|Conditional probability, definition

We can formalize the definition of conditional probability so that the mathematics matches our intuition.
Let $B$ be an event so that $P(B)>0$. Then the conditional probability of an event $A$ given that $B$ has occurred is:
$$P(A \mid B)=\frac{P(A \cap B)}{P(B)} .$$
If $A$ and $B$ are unrelated in any way, or in other words independent, (discussed more later in the lecture), then
$$P(A \mid B)=\frac{P(A) P(B)}{P(B)}=P(A)$$
That is, if the occurrence of $B$ offers no information about the occurrence of $A$. the probability conditional on the information is the same as the probability without the information, we say that the two events are independent.

## 统计代写|统计推断作业代写statistical inference代考|Diagnostic tests

Since diagnostic tests are a really good example of Bayes’ rule in practice, let’s go over them in greater detail. (In addition, understanding Bayes’ rule will be helpful for your own ability to understand medical tests that you see in your daily life). We require a few definitions first.
Let $+$ and – be the events that the result of a diagnostic test is positive or negative respectively Let $D$ and $D^{c}$ be the event that the subject of the test has or does not have the disease respectively
The sensitivity is the probability that the test is positive given that the subject actually has the disease, $P(+\mid D)$

The specificity is the probability that the test is negative given that the subject does not have the disease, $P\left(-\mid D^{c}\right)$
So, conceptually at least, the sensitivity and specificity are straightforward to estimate. Take people known to have and not have the disease and apply the diagnostic test to them. However, the reality of estimating these quantities is quite challenging. For example, are the people known to have the disease in its later stages, while the diagnostic will be used on people in the early stages where it’s harder to detect? Let’s put these subtleties to the side and assume that they are known well.
The quantities that we’d like to know are the predictive values.
The positive predictive value is the probability that the subject has the disease given that the test is positive, $P(D \mid+)$
The negative predictive value is the probability that the subject does not have the disease given that the test is negative, $P\left(D^{c} \mid-\right)$
Finally, we need one last thing, the prevalence of the disease – which is the marginal probability of disease, $P(D)$. Let’s now try to figure out a PPV in a specific setting.

## 广义线性模型代考

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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。