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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|Validation and Scoring Rules

If elicitation from experts is difficult, then validation of their predictions and estimates can be even more challenging.

If you have some data and need to assess the extent to which an expert is over or underconfident in their probability assessments, then you can use a method called a scoring rulc. $\Lambda$ ssuming we have a set of predictions from the expert and a full set of data on actual values of outcomes we can use a scoring rule to determine the extent to which the predictions deviate from the actual values.

The simplest situation is where the model is predicting an event that either happens or does not (such as Norman arriving late for work). In other words the model provides a probability, $q$, that the event happens (and hence $1-q$ that it does not). In this case there is a simple and popular scoring rule called the Brier score that can be used. For a single prediction the Brier score is simply the square of the difference between the predicted probability, $q$, and the actual outcome, $x$, which is assumed to be 1 if the event occurs and 0 if it does not, that is, $(x-q)^2$. So
If the event occurs, the Brier score is $(1-q)^2$.
If the event does not occur, the Brier score is $q^2$.
Suppose, for example, that the predicted probability for the event “Norman arrives late” is 0.1. If the event occurs then the Brier score is $0.81$, while if it does not occur the Brier score is $0.01$. The lower the score the more accurate the model. For a sequence of $n$ predictions, the Brier score is simply the mean of the scores for the individual predictions.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Some Theory on Functions and Continuous Distributions

Before we start investigating some models that use numeric nodes it is necessary to cover some basic theory and notation needed to express the ideas involved. Many of the concepts, such as joint, marginal, and conditional distributions are common to those we met in Chapters 5 and 6 when we discussed discrete variables and Bayes’ theorem.
Recall that in Chapter 5 we defined: What happens when the number of elementary states is extremely large or even infinite? In these cases we use continuous, rather than discrete, distribution functions. Although we introduced continuous distributions in Section $5.3 .1$ we are going to provide a more formal treatment here. Box $10.1$ formally defines the key notions of continuous variable, probability density function and cumulative density function. These definitions require an understanding of calculus (differentiation and integration).

Whereas with discrete probability distributions we talk in terms of the probability of a particular state of a variable $X$, with continuous distributions (as explained in Box 10.1) we are only interested in the probability that $X$ lies within a range of values $[a, b]$ rather than a single constant value. Indeed, the probability of any single constant value is zero, since in that case $a=b$, and (from Box 10.1):
$$P(a \leq X \leq b)=F(b)-F(a)=F(a)-F(a)=0$$
For the same reason for any range $[a, b]$, the same probability is generated whether the end points $a$ and $b$ are included or not (given that each end point has probability zero):
$$P(a<X \leq b)=P(a \leq X<b)=P(a \leq X \leq b)=P(a<X<b)$$
Continuous random variables adhere to the axioms of probability theory as much as discrete variables do, as shown in Box 10.2.

# 贝叶斯分析代考

## 统计代写|贝叶斯分析代写贝叶斯分析代考|关于函数和连续分布的一些理论

$$P(a \leq X \leq b)=F(b)-F(a)=F(a)-F(a)=0$$

$$P(a<X \leq b)=P(a \leq X<b)=P(a \leq X \leq b)=P(a<X<b)$$

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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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