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Laplace's Theories of Cognitive Illusions, Heuristics, and Biases 拉普拉斯关于认知幻觉、启发式和偏差的理论
Pub Date : 2018-12-01 DOI: 10.2139/ssrn.3149224
J. Miller, A. Gelman
In his book from the early 1800s, Essai Philosophique sur les Probabilités, the mathematician Pierre-Simon de Laplace anticipated many ideas developed in the 1970s in cognitive psychology and behavioral economics, explaining human tendencies to deviate from norms of rationality in the presence of probability and uncertainty. A look at Laplace's theories and reasoning is striking, both in how modern they seem and in how much progress he made without the benefit of systematic experimentation. We argue that this work points to these theories being more fundamental and less contingent on recent experimental findings than we might have thought.
数学家皮埃尔-西蒙·德·拉普拉斯(Pierre-Simon de Laplace)在他19世纪初的著作《论概率的哲学》(Essai Philosophique sur les probabilit)中预测了20世纪70年代认知心理学和行为经济学中发展起来的许多观点,解释了人类在概率和不确定性面前偏离理性规范的倾向。看看拉普拉斯的理论和推理是惊人的,既因为它们看起来是多么现代,也因为他在没有系统实验的情况下取得了多大的进步。我们认为,这项工作指出,这些理论比我们想象的更基本,更少依赖于最近的实验发现。
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引用次数: 6
Weakly Monotonic Preference Relations Representable by Concave Utility Functions - It's Easy 用凹效用函数表示的弱单调偏好关系——很简单
Pub Date : 2017-12-26 DOI: 10.2139/ssrn.3088441
S. Lahiri
In this paper we provide conditions under which a preference relation can be represented by concave utility functions. The condition follows naturally from a proof of a theorem about representability of continuous and weakly monotonic preference relations by continuous and weakly increasing utility functions due to Wold (1943). For continuous and homothetic (hence weakly monotonic) preference relations our sufficient condition for the existence of a numerical representation by a concave utility function is also a necessary condition for such a numerical representation. In fact we are able to obtain a necessary condition for numerical representation of a homothetic preference relation by a concave utility function which we call global concavifiability and which is much stronger than concavifiability. On the way, we pick up the result, that all homothetic and continuous preference relations which are convex are numerically representable by concave utility functions.
本文给出了偏好关系可以用凹效用函数表示的条件。这个条件从Wold(1943)用连续和弱递增效用函数证明连续和弱单调偏好关系的可表征性定理中自然得出。对于连续齐次(弱单调)偏好关系,凹效用函数的数值表示存在的充分条件也是该数值表示存在的必要条件。事实上,我们能够通过一个凹效用函数来获得一个同质偏好关系的数值表示的必要条件,我们称之为全局可凹性,它比可凹性强得多。在此过程中,我们得到了一个结果,即所有凸的同质和连续偏好关系都可以用凹效用函数来表示。
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引用次数: 0
The Fiction of Full BEKK Full BEKK的虚构
Pub Date : 2017-01-15 DOI: 10.2139/ssrn.2995461
Chia‐Lin Chang, M. McAleer
The purpose of the paper is to show that univariate GARCH is not a special case of multivariate GARCH, specifically the Full BEKK model, except under parametric restrictions on the off-diagonal elements of the random coefficient autoregressive coefficient matrix, provides the regularity conditions that arise from the underlying random coefficient autoregressive process, and for which the (quasi-) maximum likelihood estimates have valid asymptotic properties under the appropriate parametric restrictions. The paper provides a discussion of the stochastic processes, regularity conditions, and asymptotic properties of univariate and multivariate GARCH models. It is shown that the Full BEKK model, which in practice is estimated almost exclusively, has no underlying stochastic process, regularity conditions, or asymptotic properties.
本文的目的是证明单变量GARCH不是多元GARCH的特例,特别是Full BEKK模型,除了在随机系数自回归系数矩阵的非对角元素的参数限制下,提供了由潜在随机系数自回归过程产生的正则性条件。并且在适当的参数限制下,(拟)极大似然估计具有有效的渐近性质。本文讨论了单变量和多变量GARCH模型的随机过程、正则性条件和渐近性质。结果表明,在实际中几乎完全估计的Full BEKK模型没有潜在的随机过程、正则性条件或渐近性质。
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引用次数: 2
Cooperative Learning by Student Teams - Achievement Divisions Method (STAD) in Statistic Learning of St. Theresa International College's Students in Nakhorn Nayok Province, Thailand 学生团队合作学习——成绩划分法(STAD)在泰国Nakhorn Nayok省圣德蕾莎国际学院学生统计学习中的应用
Pub Date : 2016-10-07 DOI: 10.2139/ssrn.2849350
Bandyopadhyay Dwiptendra, Vichian Puncreobutr
The objective of this Research was to compare the average of exercises and the Achievement of Statistic Learning between the Cooperative Learning by Student Teams-Achievement Divisions method (STAD) and the normal study method. The experimental were selected into 2 groups of 40 students of Business Administration Faculty in Academic Year 2015, St. Theresa International College. The assessment was done and stated that:1) The significant of exercise average in Cooperative Learning by Student Teams-Achievement Divisions method (STAD) higher than the normal study method .01;2) The Achievement of Statistic Learning in Cooperative Learning by Student Teams-Achievement Divisions method (STAD) higher than the normal study method .01.
本研究的目的是比较学生团队-成绩划分法(STAD)与普通学习法合作学习的练习平均值和统计学习成绩。实验以圣德蕾莎国际学院2015学年工商管理学院学生为对象,分为两组,每组40人。结果表明:1)学生团队-成绩分组法(STAD)在合作学习中练习平均的显著性高于正常学习法(0.01);2)学生团队-成绩分组法(STAD)在合作学习中统计学习的成就高于正常学习法(0.01)。
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引用次数: 0
The Philosophical Implications of Set Theory in Infinity 无穷中集合论的哲学含义
Pub Date : 2016-07-27 DOI: 10.2139/ssrn.2815293
K. Lam
What does the term “Infinity” mean? There are mathematical, physical and metaphysical definitions of the concept of limitlessness. This study will focus on the scription of the three philosophical foundations of mathematics – formalism, intuitionism and logicism – in set theory. Examples will also be provided of the concept of infinity for these three schools of thought. However, none of them cannot prove whether there is an infinite set or the existence of infinity. It forms the foundational crisis of mathematics. Further elaboration on these schools of philosophy leads to the ideas of actual, potential and absolute boundlessness. These correspond to three basic aforementioned definitions of infinity. Indeed for example, by using Basic Metaphor Infinity, cognitive mechanisms such as conceptual metaphors and aspects, one can appreciate the transfinite cardinals’ beauty fully (Nũnez, 2005). This implies the portraiture for endless is anthropomorphic. In other words, because there is a connection between art and mathematics through infinity, one can enjoy the elegance of boundlessness (Maor, 1986). Actually, in essence this is what mathematics is: the science of researching the limitless.
“无限”是什么意思?无限的概念有数学的、物理的和形而上学的定义。本研究将著重于描述集合论中数学的三个哲学基础——形式主义、直觉主义和逻辑主义。本文还将为这三种思想流派提供无限概念的例子。然而,它们都不能证明是否有一个无穷集或无穷存在。它构成了数学的基本危机。对这些哲学流派的进一步阐述,可以得出现实的、潜在的和绝对的无界的概念。这些对应于前面提到的无限的三个基本定义。事实上,例如,通过使用基本隐喻无限,认知机制,如概念隐喻和方面,人们可以充分欣赏超有限基数的美(Nũnez, 2005)。这就暗示了无尽的肖像是拟人化的。换句话说,因为艺术与数学之间存在着无限的联系,所以人们可以享受到无限的优雅(Maor, 1986)。实际上,本质上这就是数学:研究无限的科学。
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引用次数: 3
Hypercubes and the Future 超立方体和未来
Pub Date : 2016-05-07 DOI: 10.2139/ssrn.2776969
P. Cottrell
This paper will provide information on what a hypercube is and how to use them in graphing the financial markets, especially in the Poseidon software that I am developing. What types of hypercubes are there? How to describe the market in higher dimensions? What are the common variables to use in a hypercube? These questions will be explored and expounded upon. Lately, an exploration of future research in quantitative finance is presented, especially in the realm of artificial intelligence and virtual reality.
本文将提供关于什么是超立方体以及如何在绘制金融市场图形时使用它们的信息,特别是在我正在开发的Poseidon软件中。超立方体有哪些类型?如何用更高的维度来描述市场?在超立方体中使用的常见变量是什么?这些问题将加以探讨和阐述。最近,人们对定量金融的未来研究进行了探索,特别是在人工智能和虚拟现实领域。
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引用次数: 0
Transcendental Analysis of Mathematics: The Transcendental Constructivism (Pragmatism) as the Program of Foundation of Mathematics 数学的先验分析:作为数学基础课程的先验建构主义(实用主义)
Pub Date : 2015-10-20 DOI: 10.2139/ssrn.2676626
S. Katrechko
Kant's transcendental philosophy (transcendentalism) is associated with the study and substantiation of objective validity both “a human mode of cognition” as whole, and specific kinds of our cognition (resp. knowledge) [KrV, B 25]. This article is devoted to Kant’s theory of the construction of mathematical concepts and his understanding (substantiation) of mathematics as cognition “through construction of concepts in intuition” [KrV, B 752] (see also: “to construct a concept means to exhibit a priori the intuition corresponding to it”; [KrV, Â 741]). Unlike the natural sciences the mathematics is an abstract – formal cognition (knowledge), its thoroughness “is grounded on definitions, axioms, and demonstrations” [KrV, B 754]. The article consequently analyzes each of these components. Mathematical objects, unlike the specific ‘physical’ objects, have an abstract character (a–objects vs. the–objects) and they are determined by Hume’s principle (Hume – Frege principle of abstraction). Transcendentalism considers the question of genesis and ontological status of mathematical concepts. To solve them Kant suggests the doctrine of schematism (Kant’s schemata are “acts of pure thought" [KrV, B 81]), which is compared with the contemporary theories of mathematics. We develop the dating back to Kant original concept of the transcendental constructivism (pragmatism) as the as the program of foundation of mathematics. “Constructive” understanding of mathematical acts is a significant innovation of Kant. Thus mathematical activity is considered as a two-level system, which supposes a “descent” from the level of rational under-standing to the level of sensual contemplation and a return “rise”. In his theory Kant highlights ostensive (geometric) and symbolic (algebraic) constructing. The article analyses each of them and shows that it is applicable to modern mathematics, in activity of which both types of Kant's constructing are intertwined
康德的先验哲学(先验主义)与客观有效性的研究和证实有关,既包括整体的“一种人类的认知方式”,也包括我们的特定的认知方式(见第2章)。知识)[KrV, B 25]。本文致力于探讨康德关于数学概念建构的理论,以及他对数学作为“通过概念在直觉中的建构”的认知的理解(实证化)[KrV, B 752](另见:“建构一个概念意味着先验地展示与之相对应的直觉”;[KrV, Â 741])。与自然科学不同,数学是一种抽象的形式认知(知识),它的彻彻性“建立在定义、公理和论证的基础上”[KrV, B 754]。因此,本文将分析每一个组成部分。数学对象与具体的“物理”对象不同,具有抽象的特征(a-objects vs - the - objects),它们是由休谟原则(休谟-弗雷格抽象原则)决定的。先验主义考虑数学概念的起源和本体论地位问题。为了解决这些问题,康德提出了模式主义学说(康德的模式是“纯粹思维的行为”[KrV, B 81]),并将其与当代数学理论进行了比较。我们发展了可以追溯到康德原始概念的先验建构主义(实用主义)作为数学基础的纲领。对数学行为的“建设性”理解是康德的一项重大创新。因此,数学活动被认为是一个两级系统,它假设从理性理解的水平“下降”到感性沉思的水平,并返回“上升”。在他的理论中,康德强调了明示(几何)和象征(代数)的建构。本文分析了这两种类型,并指出它适用于现代数学,在现代数学的活动中,这两种类型的康德建构是交织在一起的
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引用次数: 0
Microeconomic Optimization of a Retail Outlet: Combinatorial and Probability Theory Methods 零售网点的微观经济优化:组合与概率论方法
Pub Date : 2015-04-12 DOI: 10.2139/ssrn.2593471
Savva Shanaev, Mikhail Vasenin
In this article we develop a completely new method of microeconomic optimization of a retail outlet. It shows how many substitute goods of each kind a firm should purchase within a trading period in order to maximize its profit given the purchase prices, trade margins and the preference structure of the customer base (i.e. a share of potential customers who prefer good A to good B, a share of customers who prefer good B to good A and an indifferent, "neutral" share, respectively). The element of uncertainty emerges due to the fact that the order in which the customers come to the outlet is not defined in advance. The method uses combinatorics and probability theory. The practical application of the method can be, particularly, airline meal optimization.
本文提出了一种全新的零售网点微观经济优化方法。它显示了在给定购买价格、交易利润率和客户基础偏好结构(即,相对于产品B,更喜欢产品a的潜在客户份额,相对于产品a,更喜欢产品B的客户份额和一个无关的、“中性”的份额)的情况下,企业在一个交易期内应该购买多少种替代产品,以实现利润最大化。不确定性因素的出现是由于顾客到达销售点的顺序没有事先确定。该方法运用了组合学和概率论。该方法的实际应用,特别是航空公司的膳食优化。
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引用次数: 0
Cross-Efficiency Aggregation by OWA Operator Weights with Fuzzy Data 模糊数据下OWA算子权重的交叉效率聚合
Pub Date : 2014-02-09 DOI: 10.2139/ssrn.2392955
F. Adjogble, Elham Rostamiyan
Cross-efficiency evaluation is an effective way of ranking decision-making units (DMUs) in data envelopment analysis (DEA) and can be performed with different formulations (aggressive or benevolent), secondary goals and models. In this paper we use neutral formulation for cross-efficiency aggregation. The neutral formulation determines one set of input and output weights for each DMU from its own point of view without being aggressive or benevolent to the other DMUs. Existing approaches for cross-efficiency evaluation are mainly focused on the calculation of cross-efficiency matrix, but pay little attention to the aggregation of the efficiencies in the cross-efficiency matrix. This paper focuses on the use of ordered weighted averaging (OWA) operator weights for cross-efficiency aggregation. The use of OWA operator weights allows the decision maker (DM)’s optimism level towards the best relative efficiencies. But in real world, we are often conformed to ambiguous and uncertain data. So, there is an undeniable need for fuzzy logic to evaluate the efficiency unit.
交叉效率评价是数据包络分析(DEA)中对决策单元(dmu)进行排序的有效方法,可以采用不同的公式(侵略性或仁慈性)、次要目标和模型进行。本文采用中性公式进行交叉效率聚合。中性公式从自己的角度确定每个DMU的一组输入和输出权重,而不会对其他DMU具有侵略性或仁慈性。现有的交叉效率评价方法主要集中在交叉效率矩阵的计算上,而很少关注交叉效率矩阵中效率的集合。本文重点研究了在交叉效率聚合中使用有序加权平均(OWA)算子权值。OWA操作员权重的使用允许决策者(DM)对最佳相对效率的乐观程度。但在现实世界中,我们经常受到模棱两可和不确定的数据的影响。因此,利用模糊逻辑对效率单元进行评价是不可否认的。
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引用次数: 0
The Precision Effect: How Numerical Precision Influences Everyday Judgments 精确度效应:数值精确度如何影响日常判断
Pub Date : 2013-06-01 DOI: 10.2139/ssrn.2229833
Manoj. T. Thomas, Joowon Park
Numerical precision – unusually precise or sharp numbers – can trigger heuristic processing and influence judgments. Numerical precision triggers heuristic processing because it causes computational difficulty or encoding difficulty. The authors propose that the discrepancy attribution model can offer a parsimonious explanation for the effects of numerical precision on everyday judgments.
数值精度-异常精确或尖锐的数字-可以触发启发式处理并影响判断。数值精度会导致计算困难或编码困难,从而触发启发式处理。作者提出,差异归因模型可以为数值精度对日常判断的影响提供一个简洁的解释。
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引用次数: 9
期刊
CSN: Mathematics (Topic)
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