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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|Static Discretization

The model in Figure $9.1$ of Chapter 9 contained a node for rainfall, $R$, which represents the amount of rain (measured in millimeters) falling in a given day. We defined the set of states of a variable called rainfall to be “none,” “< $<2 \mathrm{~mm}$,” “2-5 mm,” ” $>5 \mathrm{~mm}$.” In mathematical notation this set of states is written as the following intervals:
$$\Psi_R:{[0],(0-2],(2-5],(5 \text {, infinity) }}$$

Since the objective of the model was to predict the probability of water levels rising and causing a flood, it is clear that any information about rainfall is very important. But the problem is that, because of the fixed discretization, the resulting model is insensitive to very different observations of rainfall. For example:

• The observation $2.1 \mathrm{~mm}$ of rain has exactly the same effect on the model as an observation of $5 \mathrm{~mm}$ of rain. Both of these observations fall into the interval $(2,5]$.
• The observation $6 \mathrm{~mm}$ of rain has exactly the same effect on the model as an observation of $600 \mathrm{~mm}$ of rain. Both of these observations fall into the interval (5, infinity).
The obvious solution to this problem is to increase the granularity of the discretization. Including AgenaRisk there is automated support to enable you to do this relatively casily. Normally, this involves declaring the node to be of type continuous interval and then bringing up a dialogue (Figure 10.2(a)) that enables you to easily create a set of intervals of any specified length, as shown in Figure 10.2(b).

It is also possible, of course, to add and edit states manually. Similar wizards are available for nodes that would be better declared as integer (such as a node number of defects).

The problem is that, although such tools are very helpful, they do not always solve the problem. No matter how many times we change and increase the granularity of the discretization, we inevitably come across new situations in which the level is inadequate to achieve an accurate estimate. But this is a point we will return to at the end of the section.
Whatever the discretization level chosen there are immediate benefits of defining a node that really does represent a numeric value as a numeric node rather than, say, a labeled or ranked node. Suppose, for example, that rainfall is defined as a numeric node with the set of states in Figure 10.2(b). Then when we come to define the NPT of rainfall we can use a full range of statistical and mathematical functions (Appendix $\mathrm{E}$ lists all the statistical distribution functions available in AgenaRisk). Some examples are shown in Figure 10.3.

In each case it is simply a matter of selecting the relevant distribution from a list and then stating the appropriate parameters; so, for example, the parameters of the TNormal $(5,6,0,20)$ distribution in Figure $10.3$ are, in order: mean (5), variance (6), lower bound (0), upper bound (20).
The benefits of numeric nodes are especially profound in the case where the intervals are not all cqual, as cxplaincd in Box $10.6$.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Using Dynamic Discretization

In this section we consider some example models that incorporate numeric nodes with all the different types of nodes covered in Chapter 9. The first examples show how dynamic discretization can be used to model purely predictive situations based on prior assumptions and numerical relationships between the variables in the model. We present the car costs example here to model a prediction problem, that is, to model consequence based on knowledge about causes. The next example shows how we might use the algorithm for induction, that is, as a means to learn parameters from observations, and by doing so exploiting Bayes’ theorem in reasoning from consequence to cause. The final example is more challenging and presents three ways to estimate school exam performance using a classical frequentist model and two Bayesian models.

The objective of this model, shown in Figure $10.15$, is to predict the annual running costs of a new car (automobile) from a number of assumptions. This particular example uses a number of modeling features that illustrate the flexibility and power of dynamic discretization, because it

• Shows how we can use mixture distributions conditioned on different discrete assumptions.
• Uses constant values that are then used in subsequent conditional calculations.
• Uses both conditionally deterministic functions and statistical distributions alongside discrete nodes as a complete hybrid $\mathrm{BN}$.

# 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|静态离散化

$$\Psi_R:{[0],(0-2],(2-5],(5 \text {, infinity) }}$$

## 统计代写|贝叶斯分析代写贝叶斯分析代考|采用动态离散化

.

• 展示了我们如何使用不同离散假设条件下的混合分布。
• 使用在后续条件计算中使用的常量值。
• 使用条件确定性函数和离散节点的统计分布作为完整的混合$\mathrm{BN}$ .

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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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