数学代写|随机过程统计代写Stochastic process statistics代考|STAT3061

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随机过程 用于表示在时间上发展的统计现象以及在处理这些现象时出现的理论模型,由于这些现象在许多领域都会遇到,因此这篇文章具有广泛的实际意义。

statistics-lab™ 为您的留学生涯保驾护航 在代写随机过程统计Stochastic process statistics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。我们的专家在代写随机过程统计Stochastic process statistics代写方面经验极为丰富,各种代写随机过程统计Stochastic process statistics相关的作业也就用不着说。

我们提供的随机过程统计Stochastic process statistics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
数学代写|随机过程统计代写Stochastic process statistics代考|STAT3061

数学代写|随机过程统计代写Stochastic process statistics代考|Genetic Algorithms

Genetic algorithms are among the first developed stochastic optimization methods. They were proposed by Holland (1975) and are a subtype of the so-called evolutionary algorithms. They emulate the evolution of a species, where the more capable individuals in a given population have higher chances to pass their genes to further generations. In mathematical terms, a solution $\bar{x}$ is an individual in the $\mathrm{GA}$, and a given set of solutions forms a population. One of the particularities of the GAs is that the solutions are represented in terms of chromosomes, i.e., chains containing the genetic information of each individual. That codified representation is known as genotype, whereas the “manifestation” of the genotype, i.e., the physical/mathematical system, is known as phenotype. Some examples of chromosomes are shown in Figure 3.1, where binary, integer, and alphabetic representations can be observed. The type of representation to be used depends on the problem to be solved. Each locus (position on the chain) can show different values (alleles), and each combination of locus and values represents different solutions for the objective function $\mathrm{f}(\bar{x})$. For engineering applications, codification with real numbers is more advisable because of the similarity between the genotype and the phenotype spaces (Gen and Cheng, 2000).

Once the problem has been codified, an initial solution is required to start the algorithm. The GAs function with a set of solutions in a simultaneous way, thus the initial point is indeed a population of solutions, each one with particular characteristics (i.e., different genetic information) that differentiate it from the others. The initial population is generated randomly. Then, it is necessary to evaluate the individuals on that first generation of solutions to determine which of them are good individuals and which are bad individuals. This classification is given by the so-called fitness function, which is strongly related to the objective function. Thus,for minimization, “good individuals” are those with a low value of $f(\bar{x})$. Then, a selection procedure is started. In this step, some of the individuals in the generation are selected to reproduce and give birth to the next generation, which is expected to have better characteristics than those of the previous generation. In general, the best individuals of the generation (i.e., those with the better values of $f(\bar{x})$ have higher probabilities of being selected for reproduction). Nevertheless, other individuals can also be selected to give genetic variability in the following generation, ensuring that a wider space in the feasible region is analyzed.

数学代写|随机过程统计代写Stochastic process statistics代考|Differential Evolution

Differential evolution is an evolutionary method. It shares some characteristics with the GAs. It was first proposed by Storn and Price (1997) as a strategy to solve the Chebyshev polynomial fitting problem (Shaoqiang et al., 2010). Similar to the GAs, the DE method functions with generations, where each generation comprises a number of parameter vectors representing a set of solutions. It is important to recall that DE uses a real-number representation at the parameter vectors. To start with the algorithm, an initial solution is

randomly generated. The solutions in the generation are evaluated through the fitness function, which is related to the objective function. To produce the next generation, an individual $\bar{x}{\text {SEL }}$ is randomly selected as candidate to be substituted through the crossover operation. Here, three other individuals $\left(\bar{x}{p 1}, \bar{x}{p 2}, \bar{x}{p 3}\right)$ are selected as parents, where one of the individuals will act as the main parent. Then, a fraction of the difference between the values of each variable in the other two parents is computed. Those values are added to the value of the respective variable in the main parent, which can be expressed as follows:
\left(\bar{x}{\mathrm{NEW}}\right)^{T}=\left(\bar{x}{p 1}\right)^{T}+F \times\left[\left(\bar{x}{p 2}\right)^{T}-\left(\bar{x}{p 3}\right)^{T}\right]
where $F$ is a randomly generated number and $F \in(0,1)$ (Abbass et al., 2001). The new individual $\bar{x}{\mathrm{NEW}}$ is then compared with the selected individual. If $\mathrm{f}\left(\bar{x}{\text {NEW }}\right)$ is better than $\mathrm{f}\left(\bar{x}{\text {SEL }}\right)$, then $\bar{x}{\text {SEL }}$ is replaced by $\bar{x}{\text {NEW }}$ in the population. Otherwise, $\bar{x}{\text {SEL. }}$ remains as an individual for the next generation. This operation takes place until the new generation has been completed. The procedure continues until the CC has been reached, which may imply a maximum number of generations. Figure $3.4$ shows a graphical representation of the DE method.

数学代写|随机过程统计代写Stochastic process statistics代考|Tabu Search

Tabu search is an optimization method proposed by Glover (1977, 1989). The method was originally developed to solve combinatorial problems related with scheduling and covering (Glover, 1989). One of the most important concepts, from which the method takes its name, is the so-called tabu list. The tabu list consists of a set containing some of the solutions that have been already proved. In general, the method starts with a single initial solution $\bar{x}$, setting the tabu list as empty. The initial solution is then perturbed several times to generate a number of new solutions $\bar{x}^{\prime}$, which is known as the neighborhood of $\bar{x}, N(\bar{x})$. This neighborhood can be obtained by applying a modification $m$ to the initial solution, i.e., $\bar{x}^{\prime}=\bar{x}^{\prime} \pm m$ (Fiechter, 1994). At the first steps of the algorithm, it is possible to move to a solution $f\left(\bar{x}^{\prime}\right)$, no matter if it is better than $\mathrm{f}(\bar{x})$ or not. A given number of the last obtained solutions is then added to the tabu list. The solutions in the previous iteration are then compared and the best one is selected as the new suboptimal. The new solution is then perturbed to generate another set of alternative solutions. For a next iteration, if a new solution is contained in the tabu list, it must be rejected and an alternative solution is proposed. As the iterations advance, the oldest components of the tabu list are deleted. The method continues until the stop criterion is reached, which may imply a maximum number of iterations. Figure $3.5$ presents a graphical representation of the tabu search method.

数学代写|随机过程统计代写Stochastic process statistics代考|STAT3061


数学代写|随机过程统计代写Stochastic process statistics代考|Genetic Algorithms

遗传算法是最早开发的随机优化方法之一。它们是由 Holland (1975) 提出的,是所谓进化算法的一个子类型。它们模拟了一个物种的进化,在这个物种中,给定种群中能力更强​​的个体有更高的机会将他们的基因传给后代。用数学术语来说,一个解决方案X¯是个人G一个,并且一组给定的解决方案形成一个总体。遗传算法的特点之一是解决方案以染色体的形式表示,即包含每个个体遗传信息的链。这种编码表示被称为基因型,而基因型的“表现”,即物理/数学系统,被称为表型。图 3.1 显示了一些染色体示例,其中可以观察到二进制、整数和字母表示。要使用的表示类型取决于要解决的问题。每个位点(链上的位置)可以显示不同的值(等位基因),每个位点和值的组合代表目标函数的不同解F(X¯). 对于工程应用,由于基因型和表型空间之间的相似性,使用实数编码更为可取(Gen 和 Cheng,2000)。

一旦问题被编码,就需要一个初始解决方案来启动算法。GA 以同时的方式与一组解一起起作用,因此初始点确实是一组解,每个解都具有将其与其他解区分开的特定特征(即不同的遗传信息)。初始种群是随机生成的。然后,有必要对第一代解决方案中的个体进行评估,以确定其中哪些是好个体,哪些是坏个体。这种分类由所谓的适应度函数给出,它与目标函数密切相关。因此,为了最小化,“好个体”是那些具有低价值的个体F(X¯). 然后,开始选择过程。在这一步中,选择一代中的一些个体进行繁殖并产生下一代,预计其具有比上一代更好的特征。一般来说,这一代人中最优秀的人(即那些拥有更好价值观的人)F(X¯)被选中繁殖的概率更高)。尽管如此,也可以选择其他个体在下一代中给出遗传变异性,确保分析可行区域中更广阔的空间。

数学代写|随机过程统计代写Stochastic process statistics代考|Differential Evolution

差分进化是一种进化方法。它与 GA 有一些共同的特点。它首先由 Storn 和 Price (1997) 提出作为解决切比雪夫多项式拟合问题的策略 (Shaoqiang et al., 2010)。与 GA 类似,DE 方法具有代数,其中每一代都包含许多参数向量,代表一组解。重要的是要记住 DE 在参数向量处使用实数表示。从算法开始,初始解是

随机生成。生成中的解是通过与目标函数相关的适应度函数来评估的。为了产生下一代,一个人X¯这个 通过交叉操作随机选择作为待替换的候选。在这里,另外三个人(X¯p1,X¯p2,X¯p3)被选为父母,其中一个人将作为主要父母。然后,计算其他两个父项中每个变量的值之间差异的一部分。这些值被添加到主父级中相应变量的值中,可以表示如下:

在哪里F是一个随机生成的数字,并且F∈(0,1)(阿巴斯等人,2001 年)。新个体X¯ñ和在然后与选定的个体进行比较。如果F(X¯新的 )好于F(X¯这个 ), 然后X¯这个 被替换为X¯新的 在人口中。否则,X¯这个。 仍然是下一代的个体。此操作一直进行到完成新的生成为止。该过程一直持续到达到 CC 为止,这可能意味着最大代数。数字3.4显示了 DE 方法的图形表示。

数学代写|随机过程统计代写Stochastic process statistics代考|Tabu Search

禁忌搜索是 Glover (1977, 1989) 提出的一种优化方法。该方法最初是为了解决与调度和覆盖相关的组合问题而开发的(Glover,1989)。该方法得名的最重要概念之一是所谓的禁忌列表。禁忌列表由一组包含一些已被证明的解决方案组成。通常,该方法从单个初始解决方案开始X¯,将禁忌列表设置为空。然后对初始解决方案进行多次扰动以生成许多新解决方案X¯′,这被称为邻域X¯,ñ(X¯). 这个邻域可以通过应用修改来获得米到初始解,即X¯′=X¯′±米(菲希特,1994 年)。在算法的第一步,可以移动到一个解决方案F(X¯′), 不管它是否比F(X¯)或不。然后将给定数量的最后获得的解决方案添加到禁忌列表中。然后比较上一次迭代中的解决方案,并选择最好的一个作为新的次优。然后扰动新解决方案以生成另一组替代解决方案。对于下一次迭代,如果禁忌列表中包含新的解决方案,则必须拒绝它并提出替代解决方案。随着迭代的推进,禁忌列表中最旧的组件被删除。该方法一直持续到达到停止标准,这可能意味着最大迭代次数。数字3.5提供了禁忌搜索方法的图形表示。

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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。