### 统计代写|贝叶斯网络代写Bayesian network代考|IMC012

statistics-lab™ 为您的留学生涯保驾护航 在代写贝叶斯网络Bayesian network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。我们的专家在代写贝叶斯网络Bayesian network代写方面经验极为丰富，各种代写贝叶斯网络Bayesian network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|贝叶斯网络代写Bayesian network代考| Probabilistic Representation

In the previous section we represented the interactions between Age, Sex, Education, Occupation, Residence and Travel using a DAG. To complete the BN modelling the survey, we will now specify a joint probability distribution over these variables. All of them are discrete and defined on a set of nonordered states (called levels in $\mathrm{R}$ ).

Therefore, the natural choice for the joint probability distribution is a multinomial distribution, assigning a probability to each combination of states of the variables in the survey. In the context of $\mathrm{BNs}$, this joint distribution is called the global distribution.

However, using the global distribution directly is difficult: even for small problems, such as that we are considering, the number of parameters involved is very high. In the case of this survey, the parameter set includes the 143 probabilities corresponding to the combinations of the levels of all the variables. Fortunately, we can use the information encoded in the DAG to break down the global distribution into a set of smaller local distributions, one for each variable. Recall that arcs represent direct dependencies: if there is an arc from one variable to another, the latter depends on the former. In other words, variables that are not linked by an arc are conditionally independent. As a result, we can factorise the global distribution as follows:
$$\operatorname{Pr}(A, S, E, 0, R, T)=\operatorname{Pr}(A) \operatorname{Pr}(S) \operatorname{Pr}(E \mid A, S) \operatorname{Pr}(0 \mid E) \operatorname{Pr}(R \mid E) \operatorname{Pr}(T \mid O, R)$$
Equation (1.1) provides a formal definition of how the dependencies encoded in the DAG map into the probability space via conditional independence relationships. The absence of cycles in the DAG ensures that the factorisation is well defined. Each variable depends only on its parents; its distribution is univariate and has a (comparatively) small number of parameters. The set of all the local distributions has, overall, fewer parameters than the global distribution. The latter represents a more general model than the former, because it does not make any assumption on the dependencies between the variables. In other words, the factorisation in Equation (1.1) defines a nested model or a submodel of the global distribution.

## 统计代写|贝叶斯网络代写Bayesian network代考|Learning the DAG Structure: Tests and Scores

In the previous sections we have assumed that the DAG underlying the BN is known. In other words, we rely on prior knowledge on the phenomenon we are modelling to decide which arcs are present in the graph and which are not. However, this is not always possible or desired; the structure of the DAG itself may be the object of our investigation. It is common in genetics and systems biology, for instance, to reconstruct the molecular pathways and networks underlying complex diseases and metabolic processes. An outstanding example of this kind of study can be found in Sachs et al. (2005) and will be explored in Chapter 8. In the context of social sciences, the structure of the DAG may identify which nodes are directly related to the target of the analysis and may therefore be used to improve the process of policy making. For instance, the

DAG of the survey we are using as an example suggests that train fares should be adjusted (to maximise profit) on the basis of Occupation and Residence alone.

Learning the DAG of a $\mathrm{BN}$ is a complex task, for two reasons. First, the space of the possible DAGs is very big; the number of DAGs increases superexponentially as the number of nodes grows. As a result, only a small fraction of its elements can be investigated in a reasonable time. Furthermore, this space is very different from real spaces (e.g., $\mathbb{R}, \mathbb{R}^{2}, \mathbb{R}^{3}$, etc.) in that it is not continuous and has a finite number of elements. Therefore, ad-hoc algorithms are required to explore it. We will investigate the algorithms proposed for this task and their theoretical foundations in Section 6.5. For the moment, we will limit our attention to the two classes of statistical criteria used by those algorithms to evaluate DAGs: conditional independence tests and network schrest.

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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。