物理代写|统计力学代写Statistical mechanics代考|PHYS3020

如果你也在 怎样代写统计力学Statistical mechanics这个学科遇到相关的难题,请随时右上角联系我们的24/7代写客服。

统计力学是一个数学框架,它将统计方法和概率理论应用于大型微观实体的集合。它不假设或假定任何自然法则,而是从这种集合体的行为来解释自然界的宏观行为。

statistics-lab™ 为您的留学生涯保驾护航 在代写统计力学Statistical mechanics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。我们的专家在代写统计力学Statistical mechanics代写方面经验极为丰富,各种代写统计力学Statistical mechanics相关的作业也就用不着说。

我们提供的统计力学Statistical mechanics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
物理代写|统计力学代写Statistical mechanics代考|PHYS3020

物理代写|统计力学代写Statistical mechanics代考|The Law of Large Numbers and the Frequentist

A frequentist might want to use the law of large numbers, specially in its strong form, (2.3.9) or (2.3.13), in order to define the concept of probability. That might answer the objection that, if one defines that concept as a frequency of results in the repetition of a large number of the “same” experiment, the notion of “large” is imprecise. But, if we take the limit $N \rightarrow \infty$, then “large” becomes precise.

There are two obvious objections to that answer: first of all, it is true that many idealizations are made in physics by taking appropriate limits, of infinite time intervals or infinite spatial extension, ${ }^{14}$ but it is difficult to see how a concept can be defined only through such a limit. Since the limit is never reached in nature and if the concept of probability makes no sense for finite sequences of experiments, then it cannot be used in the natural sciences.

The next objection is that statements like $(2.3 .9)$ or $(2.3 .13)$ are probabilistic statements even if they refer to events having probability one. But it is circular to define a concept by using a formula that involves that very concept.

The mathematician and defender of the frequentist interpretation, Richard von Mises, avoids referring to the law of large numbers and defines probabilities as limits of frequencies of particular attributes (like falling heads for a coin or landing on a 5 for a die) within what he calls a “collective.” [324]
A collective is defined as an unlimited sequence of observations so that:

  1. The limits of frequencies of particular attributes within the collective exist.
  2. These limits are not affected by place selection, which means that the same limit would be obtained if we choose a subsequence of the original sequence of the collective according to some rule, for example the subsequence of events indexed by even numbers or by prime numbers or by numbers that are squares of integers. Of course, the rule must be specified independently of the results of the sequence of observations.

This is a way of guaranteeing that the collective is “random”. Consider the sequence $0,1,0,1,0,1,0,1, \ldots$ The limits of frequencies of 0 ‘s and 1 ‘s is obviously $\frac{1}{2}$, but it would not be so if we chose the subsequence of events indexed by even numbers or by odd numbers. And that is a way of characterizing the sequence as nonrandom. ${ }^{15}$

物理代写|统计力学代写Statistical mechanics代考|Explanations and Probabilistic Explanations

One way to connect probabilities to the physical world is via the so-called Cournot’s principle which says that, if the probability of an event $A$ is very small, given some set of conditions $C$, then one can be practically certain that the event $A$ will not occur on a single realization of those conditions. ${ }^{20}$

Of course, the event and its probability have to be specified before doing the experiment where that event could occur. Otherwise, if one tosses one thousand

coins, we will obtain a definite sequence of heads and tails and that sequence does occur, although its a priori probability is very small: $\frac{1}{2^{\text {Doxn }}}$.

Besides, the probability assigned to $A$ must be properly chosen: if one were to assign probabilities $\left(\frac{1}{3}, \frac{2}{3}\right)$ to heads and tails and toss a thousand coins, the event $A$ defined by (2.3.2) would have a very small probability (exercise: estimate that probability), although it has a probability close to 1 if one assigns the usual probabilities $\left(\frac{1}{2}, \frac{1}{2}\right)$ to heads and tails.

Another way to state Cournot’s principle is that atypical events never occur. ${ }^{21}$ However, in reality, atypical events do occur: a series of coin tossing could give significant deviations from the $\left(\frac{1}{2}, \frac{1}{2}\right)$ frequencies. But that would mean that one has to revise one’s probabilities (and this is the basis of Bayesian updating: adjust your probabilities in light of the data).

But Cournot’s principle helps us to understand what is a probabilistic explanation of “random” physical phenomena.

A first form of scientific explanation is given by laws. If state A produces state $B$, according to deterministic laws, then the occurence of $B$ can be explained by the occurrence of $A$ and the existence of those laws. ${ }^{22}$ If $A$ is prepare in the laboratory, this kind of explanation is rather satisfactory, since the initial state A is produced by us.

But if B is some natural phenomena, like today’s weather and A is some meteorological condition yesterday, then $\mathrm{A}$ itself has to be explained, and that leads potentially to an “infinite” regress, going back in principle to the beginning of the universe. In practice, nobody goes back that far, and A is simply taken as “given”, which means that our explanations are in practice limited when we go backwards in time.

It is worth noting that there is something “anthropomorphic” even in this type of explanation: for example if $\mathrm{A}$ is something very special, one will try to explain A as being caused by anterior events that are not so special. Otherwise our explanation of B in terms of A will look unsatisfactory. Both the situations A and B and the laws are perfectly objective but the notion of explanation is “subjective” in the sense that it depends on what we, humans, regard as a valid explanation.

Consider now a situation where probabilities are involved, starting with the simplest example, coin tossing, and trying to use that example to build up our intuition about what constitutes a valid explanation.

物理代写|统计力学代写Statistical mechanics代考|Final Remarks

The opposition between the frequentist and Bayesian approaches to probability theory can be viewed, at least in some versions of that opposition, as part of a larger opposition between a certain version of empiricism and a certain version of rationalism. By this we mean that Bayesianism relies on the notion of rational (inductive) inference, which by definition, goes beyond mere analysis of data. The link to rationalism is that it trusts human reason of being able to make rational judgments that are not limited to “observations”. By contrast, frequentism is related to a form of skepticism with respect to the reliability of such judgments, in part because their answers can be ambiguous, as exemplified by Bertrand’s paradoxes.

Therefore, the frequentist will say, let’s limit the theory of probability to frequencies or to “data” that can be observed and forget about those uncertain reasonings. And that reaction has definitely an empiricist flavor. We have already explained our objections to that approach in Sect. 2.4. We will simply add here the remark that this move away from rationalism and towards some form of empiricism occurred simultaneously in different fields in the beginning of the twentieth century and was a somewhat understandable reaction to the “crises in the sciences” caused by the replacement of classical mechanics, that had been the bedrock of science for centuries, both by the theories of relativity and by quantum mechanics.
Here are some examples, besides frequentism, of such moves:

Logical positivism in the philosophy of science: in the Vienna Circle, there was a strong emphasis on observations or sense-data as being the only sort of things one can meaningfully speak about or “verify”. On the other hand, the logical positivists were (rightly) reacting to the metaphysical traditions in philosophy and they were also interested in inductive logic.

Formalism in the philosophy of mathematics: while realists in the philosophy of mathematics (often called Platonists) think that mathematics studies something real (numbers or sets), formalists argued that mathematicians are just deducing theorems from axioms according to given rules, but nothing more and that the axioms and the rules do not attempt to capture some “hidden” reality.

Behaviorism in the philosophy of mind: instead of postulating some “hidden” mental structures, behaviorists insisted that on should only study the links between stimuli and reactions.

The Copenhagen interpretation of quantum mechanics: the goal of science, for Bohr, Heisenberg and their followers, as opposed to the “realists” like Einstein and Schrödinger, is not to discover the properties of some microscopic reality but only to predict “results of measurements.”

Of course, for each of these positions, there are pros and cons and various nuances of these positions and we do not intend to discuss them in detail. But what is common to them is a sort of modesty with respect to science and knowledge: let’s focus on what we know for certain: empirical frequencies, sense-data, formal manipulations, inputoutput reactions, or “measurements”. But, in doing so, one abandons the explanatory character of science.

In general, modesty is praiseworthy; the problem here is that, if it goes too far, it tends to make science devoid of meaning and therefore, of interest.

物理代写|统计力学代写Statistical mechanics代考|PHYS3020

统计力学代考

物理代写|统计力学代写Statistical mechanics代考|The Law of Large Numbers and the Frequentist

频率论者可能想要使用大数定律,特别是它的强形式(2.3.9)或(2.3.13),来定义概率的概念。这可能会回答这样的反对意见,即如果将这一概念定义为重复大量“相同”实验的结果频率,那么“大”的概念是不精确的。但是,如果我们采取限制ñ→∞,那么“大”就变得精确了。

对这个答案有两个明显的反对意见:首先,物理学中的许多理想化确实是通过采取适当的限制,无限的时间间隔或无限的空间扩展,14但是很难看出如何仅通过这样的限制来定义一个概念。由于自然界永远不会达到极限,如果概率的概念对有限的实验序列没有意义,那么它就不能用于自然科学。

下一个反对意见是这样的陈述(2.3.9)或者(2.3.13)是概率陈述,即使它们指的是概率为 1 的事件。但是通过使用包含该概念的公式来定义一个概念是循环的。

频率论解释的数学家和捍卫者理查德·冯·米塞斯(Richard von Mises)避免提及大数定律,并将概率定义为特定属性的频率限制(例如硬币掉头或骰子落在 5 上)在他的范围内。称为“集体”。[324]
集体被定义为无限的观察序列,因此:

  1. 集体中特定属性的频率限制是存在的。
  2. 这些限制不受地点选择的影响,这意味着如果我们根据某些规则选择集合的原始序列的子序列,例如由偶数或素数索引的事件的子序列或由整数平方的数字。当然,必须独立于观察序列的结果来指定规则。

这是保证集体是“随机的”的一种方式。考虑序列0,1,0,1,0,1,0,1,…0 和 1 的频率限制显然是12,但如果我们选择由偶数或奇数索引的事件的子序列,情况就不会如此。这是将序列表征为非随机的一种方式。15

物理代写|统计力学代写Statistical mechanics代考|Explanations and Probabilistic Explanations

将概率与物理世界联系起来的一种方法是通过所谓的古诺原理,它说,如果一个事件的概率一个非常小,给定一些条件C,那么实际上可以确定该事件一个不会在这些条件的单一实现上发生。20

当然,在进行可能发生该事件的实验之前,必须指定该事件及其概率。否则,如果一个人扔一千

硬币,我们将获得一个确定的正面和反面序列,并且该序列确实发生,尽管它的先验概率非常小:12多克斯 .

此外,分配给的概率一个必须正确选择:如果要分配概率(13,23)正面反面抛一千枚硬币,事件一个由 (2.3.2) 定义的概率非常小(练习:估计该概率),尽管如果分配通常的概率,它的概率接近 1(12,12)到头和尾。

陈述古诺原则的另一种方式是非典型事件永远不会发生。21然而,在现实中,确实会发生非典型事件:一系列抛硬币可能会导致明显偏离(12,12)频率。但这意味着必须修改自己的概率(这是贝叶斯更新的基础:根据数据调整概率)。

但是古诺原理帮助我们理解什么是对“随机”物理现象的概率解释。

第一种形式的科学解释是由法律给出的。如果状态 A 产生状态乙,根据确定性定律,那么乙可以解释为发生一个以及这些法律的存在。22如果一个是在实验室准备的,这种解释还是比较满意的,因为初始状态A是我们制作的。

但是如果 B 是一些自然现象,比如今天的天气,A 是昨天的一些气象条件,那么一个必须对其自身进行解释,这可能会导致“无限”倒退,原则上可以追溯到宇宙的开始。在实践中,没有人能回溯那么远,A 被简单地视为“给定的”,这意味着当我们在时间上倒退时,我们的解释在实践中是有限的。

值得注意的是,即使在这种类型的解释中,也有一些“拟人化”的东西:例如,如果一个是非常特别的东西,人们会尝试将 A 解释为由不那么特别的先前事件引起。否则,我们根据 A 对 B 的解释将看起来不能令人满意。情况 A 和 B 以及法律都是完全客观的,但解释的概念是“主观的”,因为它取决于我们人类所认为的有效解释。

现在考虑一个涉及概率的情况,从最简单的例子开始,抛硬币,并尝试使用这个例子来建立我们关于什么构成有效解释的直觉。

物理代写|统计力学代写Statistical mechanics代考|Final Remarks

概率论的频率论和贝叶斯方法之间的对立,至少在这种对立的某些版本中,可以看作是某种版本的经验主义和某种版本的理性主义之间更大对立的一部分。我们的意思是贝叶斯主义依赖于理性(归纳)推理的概念,根据定义,它超越了单纯的数据分析。与理性主义的联系在于它相信人类理性能够做出不限于“观察”的理性判断。相比之下,频率论与对此类判断可靠性的一种怀疑论形式有关,部分原因是它们的答案可能是模棱两可的,正如伯特兰悖论所例证的那样。

因此,频率论者会说,让我们将概率理论限制在可以观察到的频率或“数据”上,而忘掉那些不确定的推理。这种反应绝对具有经验主义的味道。我们已经在 Sect 中解释了我们对这种方法的反对意见。2.4. 我们将在这里简单地补充一句,从理性主义转向某种形式的经验主义在 20 世纪初同时发生在不同的领域,这是对由替代理论引起的“科学危机”的某种可以理解的反应。经典力学,几个世纪以来一直是科学的基石,无论是相对论还是量子力学。
以下是此类举动的一些示例,除了频繁性之外:

科学哲学中的逻辑实证主义:在维也纳学派中,强烈强调观察或感觉数据是唯一可以有意义地谈论或“验证”的事物。另一方面,逻辑实证主义者(正确地)对哲学中的形而上学传统做出反应,他们也对归纳逻辑感兴趣。

数学哲学中的形式主义:虽然数学哲学中的实在论者(通常称为柏拉图主义者)认为数学研究的是真实的事物(数字或集合),但形式主义者认为数学家只是根据给定的规则从公理中推导出定理,但仅此而已公理和规则并不试图捕捉一些“隐藏”的现实。

心灵哲学中的行为主义:行为主义者不应该假设一些“隐藏的”心理结构,而是坚持应该只研究刺激和反应之间的联系。

量子力学的哥本哈根解释:对于玻尔、海森堡和他们的追随者来说,与爱因斯坦和薛定谔这样的“现实主义者”相反,科学的目标不是发现某些微观现实的性质,而只是预测“测量结果” 。”

当然,对于这些职位中的每一个,这些职位都有优缺点和各种细微差别,我们不打算详细讨论它们。但他们的共同点是对科学和知识的一种谦虚:让我们专注于我们确定的知识:经验频率、感觉数据、形式操作、输入输出反应或“测量”。但是,这样做就放弃了科学的解释性。

一般来说,谦虚是值得称赞的;这里的问题是,如果它走得太远,它往往会使科学失去意义,因此失去兴趣。

物理代写|统计力学代写Statistical mechanics代考 请认准statistics-lab™

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

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题,以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法,其中不假设数据来自于由少数参数决定的规定模型;这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型(GLM)归属统计学领域,是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

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)。

有限元方法代写

有限元方法(FEM)是一种流行的方法,用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

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。

tatistics-lab作为专业的留学生服务机构,多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务,包括但不限于Essay代写,Assignment代写,Dissertation代写,Report代写,小组作业代写,Proposal代写,Paper代写,Presentation代写,计算机作业代写,论文修改和润色,网课代做,exam代考等等。写作范围涵盖高中,本科,研究生等海外留学全阶段,辐射金融,经济学,会计学,审计学,管理学等全球99%专业科目。写作团队既有专业英语母语作者,也有海外名校硕博留学生,每位写作老师都拥有过硬的语言能力,专业的学科背景和学术写作经验。我们承诺100%原创,100%专业,100%准时,100%满意。

随机分析代写


随机微积分是数学的一个分支,对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

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。

回归分析代写

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。

R语言代写问卷设计与分析代写
PYTHON代写回归分析与线性模型代写
MATLAB代写方差分析与试验设计代写
STATA代写机器学习/统计学习代写
SPSS代写计量经济学代写
EVIEWS代写时间序列分析代写
EXCEL代写深度学习代写
SQL代写各种数据建模与可视化代写

发表回复

您的电子邮箱地址不会被公开。