统计代写|贝叶斯分析代写Bayesian Analysis代考|STAT4102

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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|STAT4102

统计代写|贝叶斯分析代写Bayesian Analysis代考|Correlation Coefficient and p-Values

The correlation coefficient is a number between $-1$ and 1 that determines whether two paired sets of data (such as those for height and intelligence of a group of people) are related. The closer to 1 the more “confident” we are of a positive linear correlation and the closer to-1 the more confident we are of a negative linear correlation (which happens when, for example, one set of numbers tends to decrease when the other set increases as you might expect if you plotted a person’s age against the number of toys they possess). When the correlation coefficient is close to zero there is little evidence of any relationship.

Confidence in a relationship is formally determined not just by the correlation coefficient but also by the number of pairs in your data. If there are very few pairs then the coefficient needs to be very close to 1 or $-1$ for it to be deemed “statistically significant,” but if there are many pairs then a coefficient closer to 0 can still be considered “highly significant.”

The standard method that statisticians use to measure the “significance” of their empirical analyses is the $p$-value. Suppose we are trying to determine if the relationship between height and intelligence of people is significant and have data consisting of various pairs of values (height, intelligence) for a set of people; then we start with the “null hypothesis,” which, in this case is the statement “height and intelligence of people are unrelated.” The $p$-value is a number between 0 and 1 representing the probability that the data we have arisen if the null hypothesis were true. In medical trials the null hypothesis is typically of the form that “the use of drug X to treat disease $\mathrm{Y}$ is no better than not using the drug.”

The calculation of the $p$-value is based on a number of assumptions that are beyond the scope of this discussion, but people who need $p$-values can simply look them up in standard statistical tables (they are also computed automatically in Excel when you run Excel’s regression tool). The tables (or Excel) will tell you, for example, that if there are 100 pairs of data whose correlation coefficient is $0.254$, then the $p$-value is $0.01$. This means that there is a 1 in 100 chance that we would have seen these observations if the variables were unrelated.
A low $p$-value (such as $0.01$ ) is taken as evidence that the null hypothesis can be “rejected.” Statisticians say that a $p$-value of $0.01$ is “highly significant” or say that “the data is significant at the $0.01$ level.”

A competent researcher investigating a hypothesized relationship will set a $p$-value in advance of the empirical study. Typically, values of either $0.01$ or $0.05$ are used. If the data from the study results in a $p$-value of less than that specified in advance, the researchers will claim that their study is significant and it enables them to reject the null hypothesis and conclude that a relationship really exists.

统计代写|贝叶斯分析代写Bayesian Analysis代考|Spurious Correlations

Although the preceding examples illustrate the danger of reading too much into dubious correlations between variables, the relationships we saw there did not arise purely by chance. In each case some additional common factors helped explain the relationship.

But many studies, including unfortunately many taken seriously, result in claims of causal relationships that are almost certainly due to nothing other than pure chance.

Although nobody would seriously take measures to stop Americans drinking beer in order to reduce Japanese child mortality, barely a day goes by when some decision maker or another somewhere in the world takes just as irrational a decision based on correlations that turn out to be just as spurious.

For example, on the day we first happened to be drafting this section (16 March 2009) the media was buzzing with the story that working night shifts resulted in an increased risk of breast cancer. This followed a World Health Organization study and it triggered the Danish government to make compensation awards to breast cancer sufferers who had worked night shifts. It is impossible to state categorically whether this result really is an example of a purely spurious correlation. But it is actually very simple to demonstrate why and how you will inevitably find a completely spurious correlation in such a study-which you might then wrongly claim is a causal relationship-if you measure enough things.

统计代写|贝叶斯分析代写Bayesian Analysis代考|STAT4102


统计代写|贝叶斯分析代写Bayesian Analysis代考|Correlation Coefficient and p-Values

相关系数是一个介于−1和 1 确定两组数据(例如一组人的身高和智力)是否相关。越接近 1,我们对正线性相关越“自信”,越接近 -1,我们对负线性相关越有信心(例如,当一组数字趋于减少而另一组数字趋于减少时,就会发生这种情况)如果您将一个人的年龄与他们拥有的玩具数量进行对比,那么您可能会期望设置增加)。当相关系数接近零时,几乎没有任何关系的证据。

关系的置信度不仅取决于相关系数,还取决于数据中的对数。如果对很少,则系数需要非常接近 1 或−1因为它被认为是“统计显着的”,但如果有很多对,那么接近 0 的系数仍然可以被认为是“高度显着的”。

统计学家用来衡量其实证分析的“重要性”的标准方法是p-价值。假设我们正在尝试确定人的身高和智力之间的关系是否显着,并且拥有由一组人的各种值对(身高、智力)组成的数据;然后我们从“零假设”开始,在这种情况下,它是“人的身高和智力无关”的陈述。这p-value 是一个介于 0 和 1 之间的数字,表示如果原假设为真,我们出现的数据的概率。在医学试验中,零假设的典型形式是“使用药物 X 治疗疾病是还不如不吃药。”

的计算p-value 是基于一些超出本讨论范围的假设,但需要的人p-values 可以简单地在标准统计表中查找它们(当您运行 Excel 的回归工具时,它们也会在 Excel 中自动计算)。例如,表格(或 Excel)会告诉您,如果有 100 对数据的相关系数为0.254,那么p-值是0.01. 这意味着如果变量不相关,我们有 100 分之一的机会看到这些观察结果。
一个低p-值(例如0.01) 被视为可以“拒绝”原假设的证据。统计学家说,p-的价值0.01是“非常重要的”或说“数据在0.01等级。”


统计代写|贝叶斯分析代写Bayesian Analysis代考|Spurious Correlations




例如,在我们第一次碰巧起草本节的那天(2009 年 3 月 16 日),媒体都在议论夜班工作会增加患乳腺癌的风险的故事。此前,世界卫生组织的一项研究触发了丹麦政府对上夜班的乳腺癌患者进行赔偿。不可能明确说明这个结果是否真的是纯粹虚假相关的一个例子。但实际上很简单,如果你测量了足够多的东西,就可以证明为什么以及如何在这样的研​​究中不可避免地发现完全虚假的相关性——然后你可能会错误地声称这是一种因果关系。

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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。