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我们提供的贝叶斯分析Bayesian Analysis及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (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|BSTA5014

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 $\mathrm{BN}$.
统计代写|贝叶斯分析代写Bayesian Analysis代考|BSTA5014



第9章图$9.1$中的模型包含一个降雨量节点$R$,它表示某一天的降雨量(以毫米为单位)。我们将名为rainfall的变量的状态集定义为“none”,“&lt;“$<2 \mathrm{~mm}$,”“2-5 mm,”“$>5 \mathrm{~mm}$ .”在数学符号中,这组状态被写成如下的间隔:
\Psi_R:{[0],(0-2],(2-5],(5 \text {, infinity) }}


对雨的观察$2.1 \mathrm{~mm}$与对雨的观察$5 \mathrm{~mm}$对模型的影响完全相同。这两个观测值都在$(2,5]$ .观察$6 \mathrm{~mm}$的雨对模型的影响与观察$600 \mathrm{~mm}$的雨对模型的影响完全相同。这两个观察结果都属于(5,无穷)的区间。这个问题的明显解决方案是增加离散化的粒度。包括AgenaRisk在内的自动化支持使您能够相对轻松地完成此工作。通常,这涉及将节点声明为连续间隔类型,然后弹出对话框(图10.2(a)),使您能够轻松创建任意指定长度的间隔集,如图10.2(b)所示。



在每一种情况下,它只是一个简单的问题,从列表中选择相关的分布,然后陈述适当的参数;例如,图$10.3$中的TNormal $(5,6,0,20)$分布的参数依次为:均值(5)、方差(6)、下界(0)、上界(20)。数值节点的好处在区间不都是cqual的情况下尤其深刻,如Box $10.6$中的cxplaincd .





  • 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$\mathrm{BN}$ .
统计代写|贝叶斯分析代写Bayesian Analysis代考

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。







术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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。