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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

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Bayes’ Theorem and Conditional Probability

From Chapter 5 it should be clear that the only thing that truly distinguishes frequentist and subjective approaches to measuring uncertainty is how we assign the initial probabilities to elementary events. We argued that, since there must always be some subjective assumptions in the initial assignment of probabilities, it was inevitable that all probability was subjective. What this means is that the probability assigned to an uncertain event $A$ is always conditional on a context $K$, which you can think of as some set of knowledge and assumptions. It is this central role of conditional probability that lies at the heart of the Bayesian approach described in this chapter. Fortunately, there is actually very little extra to introduce by way of theory.

We will present Bayes’ theorem and show it is simply an alternative method of defining conditional probability. The theorem is easily derived from Axiom $5.4$ (see Chapter 5; true Bayesians would actually use Bayes’ theorem as the axiom). The key benefit of Bayes’ theorem is that, in most situations, it provides a much more natural way to compute conditional probabilities.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|All Probabilities Are Conditional

Even when frequentists assign a probability value of $1 / 6$ to the event “rolling a 4 on a die,” they are conditioning this on assumptions of some physical properties of both the die and the way it can be rolled.

It follows therefore that any initial assignment of probability to an event $A$ is actually a statement about conditional probability. Hence, although we have used the terminology $P(A)$ it would be more accurate to write it as $P(A \mid K)$, where $K$ is the background knowledge or context.

In practice, if the same context $K$ is assumed throughout an analysis, then it makes sense to simply write $P(A)$ rather than $P(A \mid K)$.

Since the focus of this book is on risk in practice, rather than in casinos or theoretical games of chance, most of the events for which we have to assign an initial probability have no reasonable frequentist approach for doing so. We are therefore forced to use at least some subjective judgment. This is why a subjective probability $P(A)$ is often referred to as a “degree of belief.” However, we are driven by a quest for improvement. Having started with some initial probability assignment for an event $A$, we look for, or observe, evidence that can help us revise the probability (our degree of belief in $A$ ). In fact we all do this every day of our lives in both mundane and routine, as well as important, decision making.

# 贝叶斯分析代考

## 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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