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贝叶斯统计学是一个使用概率的数学语言来描述认识论的不确定性的系统。在 “贝叶斯范式 “中,对自然状态的相信程度是明确的;这些程度是非负的,而对所有自然状态的总相信是固定的。

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我们提供的贝叶斯统计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|贝叶斯统计代写Bayesian statistics代考|FNR6560

统计代写|贝叶斯统计代写Bayesian statistics代考|THE INDUCTION RULE

It is considered a truism that not all inferences are deductive. Arguments which compel assent, granted their premisses, are said to be limiting cases of the more general class of those whose premisses support their conclusions inconclusively. Such arguments are variously labelled ‘inductive’, ‘informative’, or ‘probable’. The conclusions of deductive arguments from true premisses are invariably true, while conclusions of probable arguments from true premisses are said to be ‘for the most part true’.. One speaks also of ‘arguments by analogy’, ‘statistical syllogisms’, and the like – terms which further argue that induction and deduction are but two sides of the same inferential coin.

Whatever the rubric preferred, non-deductive inferences have notoriously eluded precise characterisation. In particular, no clear-cut analogue of the semantical concept of validity has emerged for inductive arguments. This, despite heeroic attempts of Carnap, Hempel and others to extend the deductive concept of implication to an inductive concept of partial implication or confirmation. $^2$

Quite distinguishable from the work of the Carnapians, an older tradition persists which grounds all non-demonstrative inference on a single principle, the induction rule. Classic formulations of it assert that events conjoined in the past are likely to be conjoined in the future, that like causes have like effects, or that generalizations are the more probable the greater the number of their attested cases. Under the first of these formulations, the principle constitutes an organon of discovery, but it has also been thought to provide a rule of estimation (Reichenbach’s ‘straight rule’), a measure of confirmation (as in the third formulation), and a method of computing predictive probabilities. Only the foundation upon which it rests has been regarded as obscure and standing in need of elucidation. This is the celebrated problem of justifying induction. Otherwise put, the problem is to explain why ‘inductive methods’ work. But it is not clear just what has worked, historically or comparatively speaking.

The corpus of inductive methods can be pinned down somewhat in terms of the induction rule. But that leaves one no place to go so far as justification is concerned. For if the rule is presupposed in the extrapolation of its own successful performance, then we are back where we began – in the Humean bind. It was perhaps inevitable that someone should eventually make a merit of this ‘scandal’, and declare the very impossibility of justifying or repudiating the rule without pre-supposing it as constituting, if not justification, then ‘vindication’. 3 Related attempts to unravel Hume’s knot have argued justification is uncalled for, that “it is an analytic proposition… that … the evidence for a generalization is strong in proportion as the number of favorable instances … is great”. ${ }^4$ To ask whether it is reasonable to place reliance on the induction rule, the attempted dissolution continues, “is like asking whether it is reasonable to proportion the degree of one’s convictions to the strength of the evidence”.

统计代写|贝叶斯统计代写Bayesian statistics代考|THE IMPORT OF DATA

Classical formulations omit reference to background knowledge and so pose a spurious optimization problem: there is no optimal inductive method that depends only on frequency counts. For frequency counts have no import whatever in abstraction from a probability model. Broadly speaking, inductive reasoning allows us to base conclusions about the future behavior of a process on its past behavior. But the import of data about the past for the future is a function of the laws in accordance with which the process develops.

Polya urn models nicely illustrate this point. Imagine an urn containing $b$ black and $r$ red balls. A ball is drawn at random and replaced. But in addition, $c$ balls of the color drawn and $d$ balls of the opposite color are placed in the urn. A new drawing is made from the urn, now containing $b+r+c+d$ balls, and the procedure repeated. ${ }^6$ In Polya’s original scheme, $d=0$ and $c>0$, so that the drawing of either color increases the probability that the same color will be drawn next. This gives a rough model of contagion, where the quotient $c /(b+r)$ measures the rate of contagion. Other bounds on the random sampling without replacement, terminating after $b+r$ steps.

Now it should be clear that a given relative frequency of black balls on past drawings from a Polya urn can connote either an increase or a decrease in the probability of drawing a black ball on the ensuing trial, depending on the specifications of the parameters $b, r, c, d$. Nevertheless, by the lights of the induction rule, an abstract pattern of trial outcomes, a binary sequence, would have the same import for the future development of a process evincing fatigue as it would for a contagious process. For the trial outcomes are all that the induction rule takes explicitly into account. But in a learning experiment, for example, the probability of a correct response will usually increase with each correct response, while the probability of an incorrect response will decrease with each incorrect response, particularly if responses are corrected or reinforced. We are not merely iterating the truism that probabilities are relative to data. Rather we are urging that the data themselves depend for their import on the posited model of the experiment, the theoretical lens through which the outcomes are viewed and interpreted.

统计代写|贝叶斯统计代写Bayesian statistics代考|FNR6560


统计代写|贝叶斯统计代写Bayesian statistics代考|THE INDUCTION RULE


无论首选的标题是什么,众所周知,非演绎推论都无法准确描述。特别是,对于归纳论证,还没有出现有效性语义概念的明确类似物。尽管 Carnap、Hempel 和其他人大胆尝试将蕴含的演绎概念扩展到部分蕴含或确认的归纳概念,但这一点仍然存在。2

与 Carnapians 的工作完全不同的是,一个古老的传统仍然存在,它将所有非证明推理建立在一个单一的原则上,即归纳规则。它的经典表述断言,过去结合的事件很可能在未来结合,相同的原因具有相同的结果,或者概括的可能性越大,它们的证明案例的数量就越多。在这些公式中的第一个公式中,该原理构成了一个发现器官,但它也被认为提供了一种估计规则(Reichenbach 的“直线规则”)、一种确认措施(如在第三个公式中)和一种方法计算预测概率。只有它所依赖的基础才被认为是模糊的,需要阐明。这是证明归纳合理性的著名问题。否则,问题是解释为什么“归纳方法”有效。但从历史上或相对而言,尚不清楚究竟是什么起作用了。

归纳方法的语料库可以根据归纳规则来确定。但是,就正当理由而言,这使人无处可去。因为如果规则是在其自身成功表现的推断中预设的,那么我们又回到了我们开始的地方——休谟束缚。也许不可避免的是,有人最终会为这一“丑闻”做出贡献,并宣布在不预先假设它构成(如果不是正当化的话)“辩护”的情况下,证明或否定规则是不可能的。3 解开休谟之结的相关尝试认为证明是不必要的,“这是一个分析命题…………概括的证据与有利实例的数量成比例……很大”。4要问依赖归纳规则是否合理,试图解散继续说,“就像问一个人的信念程度与证据的强度成比例是否合理”。

统计代写|贝叶斯统计代写Bayesian statistics代考|THE IMPORT OF DATA


Polya 骨灰盒模型很好地说明了这一点。想象一个包含b黑色和r红球。随机抽取一个球并替换。但除此之外,C绘制的颜色的球和d相反颜色的球被放置在骨灰盒中。用瓮制作了一张新画,现在包含b+r+C+d球,并重复该过程。6在波利亚最初的计划中,d=0和C>0, 使得绘制任何一种颜色都会增加下一次绘制相同颜色的概率。这给出了一个粗略的传染模型,其中商C/(b+r)衡量传染率。无放回随机抽样的其他界限,终止于b+r脚步。

现在应该清楚的是,过去从 Polya 瓮中绘制的黑球的给定相对频率可能意味着在随后的试验中绘制黑球的概率增加或减少,具体取决于参数的规范b,r,C,d. 然而,根据归纳规则,试验结果的抽象模式(二进制序列)对于证明疲劳的过程的未来发展与传染性过程具有相同的重要性。因为试验结果是归纳规则明确考虑的全部。但是在学习实验中,例如,正确响应的概率通常会随着每个正确响应而增加,而错误响应的概率会随着每个不正确响应而降低,尤其是在响应被纠正或强化的情况下。我们不仅仅是在重复概率与数据相关的真理。相反,我们敦促数据本身依赖于他们在假设的实验模型上的导入,

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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。