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统计推断Statistical inference机械部件通常被设计为精确地配合在一起。例如，如果一个轴被设计成在一个孔中 “滑动配合”，轴必须比孔小一点。(传统的公差可能表明，所有的尺寸都在这些预定的公差之内。然而，对实际生产的过程能力研究可能显示出具有长尾巴的正态分布）。轴和孔的尺寸通常会形成具有一些平均值（算术平均值）和标准差的正态分布。
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统计代写|统计推断作业代写Statistical inference代考|Bayes
Curiously also, little is known about Thomas Bayes himself, a Nonconformist ${ }^{3}$ minister (Dale, 1991 and Bellhouse, 2004, have compiled the available biographic minutiae). His lack of either mathematical or theological publications has occasioned
some question as to how he could have been elected to the Royal Society in 1742 ; he is, however, now credited with an anonymous 1736 paper defending Newton’s method of fluxions (calculus) against Berkeley’s attacks on it as metaphysical (Dale, 1991). His “An Essay Towards Solving a Problem in the Doctrine of Chances,” published 2 years after his death, was read to the Society by Richard Price, who, ironically, is little known today but was a hero in his time. An ardent pamphleteer for liberty, he was responsible for coining the name “United States of America” (Hacking, 1990). He declined the invitation in 1778 by the American Congress to become a citizen and to help with administering the finances of the Revolutionary War, but he was one of two men to accept an honorary LL.D. from Yale in 1781, the other being General George Washington (Pearson, 1978). Price edited Bayes’ paper for publication, replacing Bayes’ introduction with his own and adding an appendix, so it is not always clear which ideas Bayes would have supported.
Bayes approached his subject in the classical manner, with the first part of his paper comprising formal definitions and theorems of elementary probability theory. These include the basic formula for conditional probability: “If of two subsequent events [Bayes did not explain this peculiar locution] the probability of the $1 \mathrm{st}$ be $a / N$, and the probability of both together be $P / N$, then the probability of the 2 nd on the supposition the 1st happens is Pla” (Bayes, 1763, p. 379). Bayes’ probabilities here are ratios, since he defined probability as a ratio of expectations (see Chap. 3); in modern terms, if $A$ and $B$ are two events, we say
$$
P(B \mid A)=P(A \& B) / P(A) .
$$
We would also nowadays unhesitatingly write
$$
P(A \mid B)=P(A \& B) / P(B) .
$$
as formally similar. If $A$ is antecedent to $B$, however, Bayes thought the latter proposition required separate proof. In his formulation
统计代写|统计推断作业代写STATISTICAL INFERENCE代考|Laplace
Laplace’s philosophical intentions were explicitly signaled in the title of his “Mémoire sur la probabilité des causes par les événements” of 1774 , written when he was only 25 . Evidently inspired by the lottery instituted by the French government in the latter half of the eighteenth century, he posed the following problem:
If an urn contains an infinity of white and black tickets in an unknown ratio, and if $p+q$ tickets are drawn of which $p$ are white and $q$ are black, we ask the probability that in drawing a new ticket from this urn it will be white. (Laplace, 1774/ 1891, p. 30)
Laplace reasoned essentially as follows: We know nothing of the actual constitution of the urn (except that it contains at least $p$ white and $q$ black tickets), but we do know that different constitutions will give rise to our particular sample of $p+q$ with different probabilities. To each of the infinite number of possible values $x$ of the probability of drawing a white ticket, there corresponds a different constitution of the urn. Laplace argued that in the absence of knowledge favoring one ratio of black to white over another, we may assume them all equally likely. ${ }^{7}$ This assumption seemed to be a simple instance of the same principle by which elementary probabilities in gambling were derived. In the absence of evidence for bias, we assume all six sides of a die or both faces of a coin equally likely to turn up. This principle was named by Laplace the principle of insufficient reason, to compare and contrast it with Leibniz’ principle of sufficient reason.
It was meant by the latter principle that causes identical in all respects have always the same effects. On the other hand, if it is known only that the causes are alike in some respects, whereas their likeness or difference in other respects is unknown, the reason for expecting the same effect from all is insufficient. Alternatives become possible and probability replaces certainty. (Cox, 1961, pp. 102-103)
统计代写|统计推断作业代写STATISTICAL INFERENCE代考|Criticism
Whatever plausibility the Rule of Succession could claim as a tool of inductive inference derived from application to relatively “detachable” characters like the presence of a flag on a steamboat or the color of a swan. Yet attributes could also be too obviously superficial for the Rule to have any plausibility. Keynes (1921/1973) recalls that Peirce took the first five poets from a biographical dictionary and found several mathematical properties common to their ages at death (e.g., the difference of the two digits, divided by 3 , leaves a remainder of 1 ). We would not rationally give any credence to such a law even if it were confirmed for 100 cases, astonishing though such a result would be.
There was nothing in the formulation which restricted its application to surface characters, and for generalizations of more scientific interest, the application was hardly less strained. The Rule of Succession would hold, with equal authority, that, given the same sample of swans, the probability is $101 / 102$ that the next swan should have feathers, or a head. If I had never seen a swan in my life, the probability that the first I saw should be white or feathered, etc., would be $1 / 2$, and no more.
Indeed, with the concept of causality banished to metaphysics, there was no scientific way to distinguish surface from deep, or extrinsic from intrinsic, characters. With Aristotelian causes no longer to bind things together, entities became arbitrary aggregates of characteristics, to be studied by plotting joint distributions, distances between genera in multidimensional space, and so on. The mathematics for such dreams was not yet worked out, but that was to prove indeed a merely technical problem.
It was the loss of organic connection that created the skeptical problem of induction and gave it such urgency and preeminence in the philosophy of science from the mid-eighteenth century on. And it was for such a dissociated world that the Rule of Succession was made. If certainty could not be attained, with nothing but historical frequency or habitual association to support the belief that the sun will rise tomorrow or that the next piece of bread I eat will nourish me, what the Rule of Succession offered in its stead was a very precise quantification of uncertainty.
I have described this mathematical formalization of the world as a more or less necessary consequence of the disappearance of an organic world view, as all that was thereafter possible; but it is also true that the mathematical model, once established, was in turn antagonistic to organicism. The conditions for successful application of the mathematical formulas are invalidated, or at least complicated, by any special knowledge of individuals or relationships proceeding from the latter. The Rule of Succession, in particular, required for its application a perfect ignorance of possible causes of a phenomenon.
统计推断学代写
统计代写|统计推断作业代写STATISTICAL INFERENCE代考|BAYES
奇怪的是，对托马斯·贝叶斯本人知之甚少，他是一个不墨守成规的人3部长D一种一世和,1991一种nd乙和一世一世H这你s和,2004,H一种v和C这米p一世一世和d吨H和一种v一种一世一世一种b一世和b一世这Gr一种pH一世C米一世n你吨一世一种和. 他缺乏数学或神学出版物导致
关于他如何在 1742 年被选入皇家学会的一些问题；然而，他现在被认为是在 1736 年发表了一篇匿名论文，为牛顿的通量方法辩护C一种一世C你一世你s反对伯克利将其作为形而上学的攻击D一种一世和,1991. 他死后 2 年出版的“一篇关于解决机会主义问题的论文”由理查德·普赖斯（Richard Price）读给学会，讽刺的是，他今天鲜为人知，但却是他那个时代的英雄。他是一位热心的自由小册子作者，负责创造“美利坚合众国”这个名称H一种C到一世nG,1990. 1778 年，他拒绝了美国国会关于成为公民并帮助管理独立战争财政的邀请，但他是获得荣誉法学博士的两个人之一。1781 年来自耶鲁大学，另一个是乔治华盛顿将军磷和一种rs这n,1978. 普莱斯编辑了贝叶斯的论文发表，用他自己的取代了贝叶斯的介绍并添加了一个附录，所以并不总是很清楚贝叶斯会支持哪些想法。
贝叶斯以经典的方式处理他的主题，他论文的第一部分包括基本概率论的正式定义和定理。其中包括条件概率的基本公式：“如果两个后续事件乙一种是和sd一世dn这吨和Xp一世一种一世n吨H一世sp和C你一世一世一种r一世这C你吨一世这n的概率1s吨是一种/ñ, 并且两者一起的概率是磷/ñ, 那么假设第 1 次发生的第 2 次的概率是 Pla”乙一种是和s,1763,p.379. 贝叶斯的概率在这里是比率，因为他将概率定义为期望的比率s和和CH一种p.3; 用现代的话来说，如果一种和乙是两个事件，我们说
磷(乙∣一种)=磷(一种&乙)/磷(一种).
我们今天也会毫不犹豫地写
磷(一种∣乙)=磷(一种&乙)/磷(乙).
形式上相似。如果一种先于乙然而，贝叶斯认为后一个命题需要单独的证明。在他的表述中
统计代写|统计推断作业代写STATISTICAL INFERENCE代考|LAPLACE
拉普拉斯的哲学意图在他 1774 年的“Mémoire sur la probabilité des Causes par les événements”的标题中得到了明确的暗示，当时他只有 25 岁。显然受到 18 世纪下半叶法国政府推行的彩票的启发，他提出了以下问题：
如果一个瓮中包含无限多张未知比例的黑白票，并且如果p+q门票是从中抽出的p是白色和q是黑色的，我们问从这个瓮中抽一张新票的概率是白色的。大号一种p一世一种C和,1774/1891,p.30
拉普拉斯的基本推理如下：我们对骨灰盒的实际构成一无所知和XC和p吨吨H一种吨一世吨C这n吨一种一世ns一种吨一世和一种s吨$p$在H一世吨和一种nd$q$b一世一种C到吨一世C到和吨s, 但我们确实知道不同的宪法会产生我们特定的样本p+q以不同的概率。对无限数量的可能值中的每一个X在抽到白票的概率中，对应于骨灰盒的不同构成。拉普拉斯认为，在缺乏有利于黑白比例高于另一种比例的知识的情况下，我们可以假设它们都是同样可能的。7这个假设似乎是推导出赌博基本概率的同一原理的一个简单实例。在没有偏见证据的情况下，我们假设骰子的所有六个面或硬币的两个面都同样可能出现。该原理被拉普拉斯命名为“不充分理由原理”，以与莱布尼茨的“充分理由原理”进行比较和对比。
后一种原理的意思是，在所有方面都相同的原因总是具有相同的效果。另一方面，如果只知道原因在某些方面相同，而在其他方面的相似或不同之处未知，则期望从所有方面获得相同结果的理由是不充分的。替代方案成为可能，概率取代确定性。C这X,1961,pp.102−103
统计代写|统计推断作业代写STATISTICAL INFERENCE代考|CRITICISM
无论继承规则可以声称作为一种归纳推理工具的合理性，这种工具源自于对相对“可拆卸”的字符的应用，例如汽船上的旗帜或天鹅的颜色。然而，对于规则而言，属性也可能过于肤浅而没有任何合理性。凯恩斯1921/1973回忆说，皮尔士从一本传记词典中挑选了前五位诗人，并发现了他们死后年龄共有的几个数学特性和.G.,吨H和d一世FF和r和nC和这F吨H和吨在这d一世G一世吨s,d一世v一世d和db是3,一世和一种v和s一种r和米一种一世nd和r这F1. 即使100个案例得到证实，我们也不会理性地相信这样的法律，尽管这样的结果会令人惊讶。
公式中没有任何内容将其应用限制在表面特征上，并且对于更具科学意义的概括，应用几乎没有那么紧张。继承规则具有同等权威，即给定相同的天鹅样本，概率为101/102下一只天鹅应该有羽毛或头。如果我一生中从未见过天鹅，那么我看到的第一只天鹅应该是白色的或有羽毛的等等的概率是1/2，仅此而已。
事实上，随着因果关系的概念被排除在形而上学中，没有科学的方法可以区分表面与深层，或外在与内在的特征。随着亚里士多德的原因不再将事物绑定在一起，实体成为特征的任意集合，通过绘制联合分布、多维空间中属之间的距离等来研究。这种梦想的数学还没有解决，但这确实是一个纯粹的技术问题。
正是有机联系的丧失造成了对归纳的怀疑问题，并赋予它从 18 世纪中叶以来的科学哲学中如此紧迫和卓越的地位。正是为了这样一个分离的世界，制定了继承规则。如果无法获得确定性，只有历史频率或习惯性联想来支持明天太阳会升起或我吃的下一块面包会滋养我的信念，那么继承规则所提供的精确量化不确定性。
我已经将世界的这种数学形式化描述为有机世界观消失的或多或少的必然结果，因为此后一切都是可能的。但同样真实的是，数学模型一旦建立起来，反过来又与有机主义对立。成功应用数学公式的条件因个人或从后者产生的关系的任何特殊知识而无效，或者至少是复杂的。尤其是继承规则，它的应用要求完全无视现象的可能原因。
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