Monty Hall Dilemma的困难原因探讨

采用Monty Hall Dilemma的经典研究范式,探讨了大学生被试在不同提示条件下对MHD问题的解决情况,结果发现只有在条件关系提示下,MHD的作业成绩才得到了明显的改善,但是正确率也只有35.7%。这表明MHD问题困难的原因很可能是多方面的,如认为主持人的行为完全是随机事件,很难意识到参与者的最初选择与主持人打开特定盒子间的三种条件关系;多数被试作出选择的理由是非理性的,如“坚持第一选择,相信自己的直觉”;不能正确判断MHD问题的内在概率关系以及缺乏认真思考的动力等。

从广义“Monty Hall问题”谈概率统计中的计算机仿真

分析了广义"Monty Hall问题",即有a辆车和b只羊的Monty Hall问题,得到了在改变第一次的选择和不改变第一次的选择两种不同条件下赢得汽车的概率;同时利用Matlab进行了计算机仿真。理论计算和计算机仿真分析都表明改变第一次的选择更可能赢得汽车,并得到了概率增加值的理论公式。该公式表明在广义"Monty Hall问题"中,当只有一辆汽车和两只羊时,改变第一次的选择带来的概率增加值最大,这就解释了为什么现实生活中大量的类似于"Monty Hall问题"的节目或游戏往往只有三个选项,而其中只有一个是奖品。

Higher Variations of the Monty Hall Problem (3.0, 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole’s Footsteps, as Something the Brain Does

In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.

The Monty Hall Problem and beyond: Digital-Mathematical and Cognitive Analysis in Boole’s Algebra, Including an Extension and Generalization to Related Cases

The Monty Hall problem has received its fair share of attention in mathematics. Recently, an entire monograph has been devoted to its history. There has been a multiplicity of approaches to the problem. These approaches are not necessarily mutually exclusive. The design of the present paper is to add one more approach by analyzing the mathematical structure of the Monty Hall problem in digital terms. The structure of the problem is described as much as possible in the tradition and the spirit—and as much as possible by means of the algebraic conventions—of George Boole’s Investigation of the Laws of Thought (1854), the Magna Charta of the digital age, and of John Venn’s Symbolic Logic (second edition, 1894), which is squarely based on Boole’s Investigation and elucidates it in many ways. The focus is not only on the digital-mathematical structure itself but also on its relation to the presumed digital nature of cognition as expressed in rational thought and language. The digital approach is outlined in part 1. In part 2, the Monty Hall problem is analyzed digitally. To ensure the generality of the digital approach and demonstrate its reliability and productivity, the Monty Hall problem is extended and generalized in parts 3 and 4 to related cases in light of the axioms of probability theory. In the full mapping of the mathematical structure of the Monty Hall problem and any extensions thereof, a digital or non-quantitative skeleton is fleshed out by a quantitative component. The pertinent mathematical equations are developed and presented and illustrated by means of examples.

Quantum Monty Hall Problem under Decoherence

We study the effect of decoherence on quantum Monty Hall problem under the influence of amplitude damping, depolarizing, and dephasing channels. It is shown that under the effect of decoherence, there is a Nash equilibrium of the game in case of depolarizing channel for Alice＇s quantum strategy. Whereas in case of dephasing noise, the game is not influenced by the quantum channel. For amplitude damping channel, Bob＇s payoffs are found symmetrical about a decoherence of 50% and the maximum occurs at this value of decoherence for his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob＇s classical strategy remains always dominant against any choice of Alice＇s strategy.

Clarifying the Language of Chance Using Basic Conditional Probability Reasoning: The Monty Hall Problem

Clarity and preciseness in the use of language is crucial when communicating mathematical and probabilistic ideas. Lack of these can make even the simplest problem difficult to understand and solve. One such problem is the Monty Hall problem. In the past, a controversy was stirred among professional mathematicians when trying to reach a consensus on a solution to the problem. The problem still creates confusion among some of those who are asked to solve it for the first time. We purport to demonstrate the use of more precise language of basic conditional probability could have prevented the controversy.

Maximum Entropy and Bayesian Inference for the Monty Hall Problem

We devise an approach to Bayesian statistics and their applications in the analysis of the Monty Hall problem. We combine knowledge gained through applications of the Maximum Entropy Principle and Nash equilibrium strategies to provide results concerning the use of Bayesian approaches unique to the Monty Hall problem. We use a model to describe Monty’s decision process and clarify that Bayesian inference results in an “irrelevant, therefore invariant” hypothesis. We discuss the advantages of Bayesian inference over the frequentist inference in tackling the uneven prior probability Monty Hall variant. We demonstrate that the use of Bayesian statistics conforms to the Maximum Entropy Principle in information theory and Bayesian approach successfully resolves dilemmas in the uneven probability Monty Hall variant. Our findings have applications in the decision making, information theory, bioinformatics, quantum game theory and beyond.

洪都拉斯Monty Farms公司被准许销售甘薯

近日,洪都拉斯Monty Farms公司同路易斯安那州立大学签署协议,准许销售甘薯。Monty Farms公司是拉丁美洲最大的甘薯出口商。这份协议准许Monty Farms公司在中美洲和多米尼加共和国销售甘薯,甘薯品种包括Evangeline,Bellevue,Orleans,Bonita,Murasaki.Monty Farms公司主要向欧洲出口甘薯。

“直觉引导”在概率统计课堂教学中的应用

概率统计课程的特点决定了它的课堂教学中有丰富的直觉引导可用,其直觉引导主要有四种方式存在,在概率统计课堂教学中,对不同知识点应用对应的直觉引导方式,以便起到更好的课堂教学效果.

直觉在概率求解过程中的误导

通过对警察找醉汉问题和Monty Hall问题的具体分析说明:在求某个事件的概率时,如果不经过认真分析,常常会被直觉误导,同时说明了概率论原理在概率求解过程中的重要性.

关于条件概率教学的一点想法

条件概率是概率论中最重要的概念之一,本文以实例说明在条件概率教学中,如何使学生在具体问题的解决过程中完成对知识的理解和掌握以及运用。

Quantum Effects from a Simple Card Game

A well-known, classical conundrum, which is related to conditional probability, has heretofore only been used for games and puzzles. It is shown here, both empirically and formally, that the counterintuitive phenomenon in question has consequences that are far more profound, especially for physics. A simple card game the reader can play at home demonstrates the counterintuitive phenomenon, and shows how it gives rise to hidden variables. These variables are “hidden” in the sense that they belong to the past and no longer exist. A formal proof shows that the results are due to the duration of what can be thought of as a gambler’s bet, without loss of generalization. The bet is over when it is won or lost, analogous to the collapse of a wave function. In the meantime, new and empowering information does not change the original probabilities. A related thought experiment involving a pregnant woman demonstrates that macroscopic systems do not always have states that are completely intrinsic. Rather, the state of a macroscopic system may depend upon how the experiment is set up and how the system is measured even though no wave functions are involved. This obviously mitigates the chasm between the quantum mechanical and the classical.

Reggae的魅力

多年以前，当许多人开始熟悉Boh Marlev的时候，“Reggae”也随之成为他们同样熟悉的一个词汇，这种源自于牙买加具有强烈节奏感的音乐在一段时间成为时髦的代名词，而对于著名键盘演奏家Montv Alexander和吉他演奏家Ernest Ranglin而言，他们则是这一音乐的代言人。Montv和Ernest都是牙买加著名的音乐制作人。

Integrative taxonomy of the Russet Bush Warbler Locustella mandelli complex reveals a new species from central China

Background: The Russet Bush Warbler Locustella(previously Bradypterus) mandelli complex occurs in mountains in the eastern Himalayas, southern China, Vietnam, the Philippines, and Indonesia. The taxonomy has been debated,with one(L. seebohmi) to four(L. seebohmi, L. mandelli, L. montis and L. timorensis) species having been recognised.Methods: We used an integrative approach, incorporating analyses of morphology, vocalizations and a molecular marker, to re-evaluate species limits in the L. mandelli complex.Results: We found that central Chinese L. mandelli differed from those from India through northern Southeast Asia to southeast China in plumage, morphometrics and song. All were easily classified by song, and(wing + culmen)/tail ratio overlapped only marginally. Both groups were reciprocally monophyletic in a mitochondrial cytochrome b(cytb) gene tree, with a mean divergence of 1.0 ± 0.2%. They were sympatric and mostly altitudinally segregated in the breeding season in southern Sichuan province. We found that the Mt Victoria(western Myanmar) population differed vocally from other L. mandelli, but no specimens are available. Taiwan Bush Warbler L. alishanensis was sister to the L. mandelli complex, with the most divergent song. Plumage, vocal and cytb evidence supported the distinctness of the south Vietnamese L. mandelli idonea. The Timor Bush Warbler L. timorensis, Javan Bush Warbler L.montis and Benguet Bush Warbler L. seebohmi differed distinctly in plumage, but among-population song variation in L. montis exceeded the differences between some populations of these taxa, and mean pairwise cytb divergences were only 0.5–0.9%. We also found that some L. montis populations differed morphologically.Conclusions: We conclude that the central Chinese population of Russet Bush Warbler represents a new species,which we describe herein, breeding at mid elevations in Sichuan, Shaanxi, Hubei, Hunan and Guizhou provinces.The taxonomic status of the other allopatric populations is less clear. However, as they differ to a degree comparable with that of the sympatric L. mandelli and the new species, we elevate L. idonea to species status, and retain L. seebohmi and L. montis as separate species, the latter with timorensis as a subspecies. Further research should focus on different populations of L. montis and the Mt Victoria population of L. mandelli.

Biliary tract reconstruction using jejunal tube:an experimental study in dogs

BACKGROUND:To physiologically reconstruct the biliary tract,Crema et al suggested the application of the Monti principle to the biliary tract,already used in humans for the urinary tract.With this technique,a jejunal segment is transversely retubularized.This study aimed to evaluate the efficacy of jejunal tube interposition between the common bile duct and duodenum in dogs.METHODS:Thirteen dogs underwent a laparoscopic common bile duct ligature,followed by a biliodigestive connection by jejunal tube interposition after one week.The levels of glutamic-pyruvic and glutamic-oxalacetic transaminases,total bilirubins,alkaline phosphatase and gamma-glutamyltransferase were assessed before surgery and thereafter weekly until euthanasia,which was performed 6 weeks after biliodigestive connection.RESULTS:Data on 9 dogs were analyzed statistically.The dogs presented with obstructive jaundice after common bile duct ligature,as confirmed by biochemical examination.They showed a statistically significant reduction in cholestasis after biliodigestive connection by jejunal tube interposition and were healthy until the end of the experiment.CONCLUSION:A statistically significant reduction was seen in total bilirubin and canalicular enzymes(alkaline phosphatase and gamma-glutamyltransferase)in the 9 dogs 6 weeks after biliodigestive connetion by jejunal tube interposition.

改良回肠代输尿管术治疗长段输尿管缺损的临床研究

目的总结改良回肠代输尿管术（Yang－Monti术）治疗长段输尿管缺损的经验。方法回顾性分析2015年3－11月应用Yang－Monti回肠代输尿管术治疗的2例长段输尿管缺损患者的临床资料。例1，男，75岁；诊断为上段输尿管肿瘤并孤立肾，肾盂至膀胱的长度为22 cm；术前血肌酐100 μmol/L，尿素氮5.7 mmol/L，Cl－ 98 mmol/L。例2，女，41岁；诊断为左侧医源性输尿管中下段损伤，损伤段长度为15 cm；术前血肌酐70 μmol/L，尿素氮5.1 mmol/L, Cl－100 mmol/L，患肾GFR 12.7 ml/min。2例均行肠管横向重新配置的Yang－Monti回肠代输尿管术替代输尿管。2例均取距回盲部〉15 cm、低位活动度较大的回肠段，例1切取约10.0 cm,例2切取7.5 cm，保留回肠段系膜，例1关闭系膜裂孔，将回肠段拉入腹膜后腔隙；例2于降结肠系膜开窗后拉入腹膜后间隙。两例均将回肠段分为3段，每段为2.5～3.0 cm，将3段肠管沿肠管轴方向切开，再将展开的肠管片转动90°后，用4－0可吸收线连续缝合连接3段肠管片，用F16尿管作内支撑，将连接好的肠管片重新卷管，用4－0可吸收线连续缝合成肠代输尿管，使肠管长度分别变成约22 cm和18 cm。肠代输尿管内置入两根F6双J管后，近端与肾盂、输尿管断端吻合，远端与膀胱顶、膀胱后壁吻合。结果例1手术时间140 min，术中出血量200 ml。例2手术时间180 min，术中出血量220 ml。两例术中、术后均无明显并发症发生。术后3个月复查静脉肾盂造影示，肠代输尿管通畅，例1右肾积水明显改善，例2尿路引流通畅。术后6个月随访，例1血肌酐112 μmol/L，尿素氮6.1 mmol/L，Cl－106 mmol/L；例2血肌酐79 μmol/L，尿素氮5.9 mmol/L，Cl－103 mmol/L。例2术后3个月和6个月的患肾GFR分别为24.9 ml/min和22.1 ml/min。结论对于长段输尿管缺损、无法用尿路组织替代的患者，Yang－Monti回肠代输尿管术是一种可选的手术方法，该术式并发症较少，可提高患者生活质量。

德温特世界专利索引传奇50载

值此DWPI创立50周年之际,撰文重点介绍DWPI的创始人Monty Hyams的传奇故事以及DWPI的发展史,以作纪念。

Yang—Monti管与阑尾在膀胱可控性流出道应用中的疗效比较

目的 比较Yang－Monti管与阑尾在膀胱可控性尿流改道治疗中的应用疗效。 方法回顾性分析我院2009年7月至2015年12月收治的27例神经源性膀胱患儿的临床资料。男8例，女19例。年龄1.5～16.0岁，平均7.6岁。膀胱容量（203.8±126.0）ml，其中膀胱顺应性〈20 ml/ cmH2O（1 cmH2O＝0.098 kPa）者24例，术前发热性尿路感染17例，压力性尿失禁6例，排尿困难17例。27例中7例行Yang－Monti管代膀胱流出道手术（YM组），男2例，女5例；年龄4.0～16.0岁，平均6.7岁。20例行阑尾代膀胱流出道手术（AP组），男6例，女14例；年龄1.5～14.0岁，平均8.0岁。通过记录两组的3 d导尿日记及导尿情况，比较两组在平均导尿间隔、平均单次导尿量、流出道狭窄、流出道漏尿方面的差异。 结果 YM组7例中，2例行开放手术，5例行腹腔镜手术（其中2例中转开放手术）；AP组20例中，3例行开放手术，17例行腹腔镜手术（其中1例中转开放手术），两组的手术时间、术中输血例数和住院时间差异均无统计学意义（均P〉0.05）。YM组7例术后随访1～7年，平均2.4年，平均单次导尿量（239.3±76.2）ml，平均导尿间隔时间（2.8±0.9）h；其中术后随访1～3年者6例，平均导尿间隔时间（2.6±0.8）h。术后1例出现流出道狭窄，1例漏尿。AP组20例术后随访时间1～7年，平均3.0年，平均单次导尿量（257.0±67.4）ml，平均导尿间隔时间（3.9±0.9）h；其中术后随访1～3年者6例，平均导尿间隔时间（3.5±1.0）h。术后1例出现流出道狭窄，2例漏尿。两组患儿在平均单次导尿量、流出道狭窄、流出道漏尿这几项指标间的差异均无统计学意义（均P〉0.05）；两组患儿平均导尿间隔时间差异有统计学意义（P〈0.05），但术后随访1～3年的患儿平均导尿间隔时间的差异无统计学意义（P〉0.05）。结论 Yang－Monti管代流出道手术与阑尾代流出道手术术后并发症发生率相似，疗效接近，对无法用阑尾做流出道的患者，可考虑采用Yang－Monti管制作可控性膀胱流出道。