具体描述
《概率论沉思录(英文版)》将概率和统计推断融合在一起，用新的观点生动地描述了概率论在物理学、数学、经济学、化学和生物学等领域中的广泛应用，尤其是它阐述了贝叶斯理论的丰富应用，弥补了其他概率和统计教材的不足。全书分为两大部分。第一部分包括10章内容，讲解抽样理论、假设检验、参数估计等概率论的原理及其初等应用；第二部分包括12章内容，讲解概率论的高级应用，如在物理测量、通信理论中的应用。《概率论沉思录(英文版)》还附有大量习题，内容全面，体例完整。
《概率论沉思录(英文版)》内容不局限于某一特定领域，适合涉及数据分析的各领域工作者阅读，也可作为高年级本科生和研究生相关课程的教材。
《随机漫步的宇宙：混沌边缘的数学之舞》 在这部充满思想火花的著作中，我们将踏上一段探索宇宙奥秘的非凡旅程，而引领我们穿越这场旅程的，是那潜藏在万物背后，时而清晰时而模糊的“随机性”的脉络。本书并非一本枯燥的数学教科书，更非对抽象概念的冷冰冰的罗列。相反，它是一场盛大的思想实验，一次对我们赖以生存的现实世界的深度透视，一场关于“可能性”与“必然性”之间微妙平衡的沉思。 想象一下，黎明时分，第一缕阳光穿透晨雾，洒在露珠晶莹的草叶上。每一颗露珠都折射出独一无二的光芒，那细微的差异，是否也遵循着某种不可见的法则？又或者，当一群蝴蝶在热带雨林中翩翩起舞，它们的翅膀每一次扇动，是否都在为下一次飞行，甚至远在千里之外的季风，埋下伏笔？《随机漫步的宇宙》便是要带你一同去探寻这些隐藏在日常现象之下的“概率之舞”。 本书的开篇，我们将从“偶然”的哲学意涵入手，审视人类数千年来对命运、巧合与不可预测性的思考。从古希腊哲学家对“混沌”与“秩序”的辩论，到中世纪炼金术士对元素组合的模糊尝试，再到近代科学革命对精确测量与因果关系的追求，历史的长河中，我们对“随机”的理解从未停止演变。我们将追溯那些曾经模糊不清的直觉，如何在科学的严谨审视下，逐渐凝聚成具有普适性的数学语言。 随后，我们将深入探讨“概率”这一核心概念的数学基石。这并非要求读者具备深厚的数理功底，而是以一种启发式的、直观的方式，引导大家理解概率的本质：它是对不确定性的一种量化描述，是对未来可能发生事件的一种度量。我们将从最简单的抛硬币、掷骰子等经典例子出发，逐步揭示“独立事件”、“条件概率”等概念的内在逻辑。例如，为何每一次抛硬币的结果似乎都与上一次无关，而连续出现多次同一面的可能性又为何如此之低？这些看似简单的游戏，背后蕴含着深刻的数学原理，它们是我们理解更复杂随机现象的基石。 本书的一个重要主题，便是“随机过程”。我们将目光从孤立的事件，转向连续发生、相互关联的事件序列。想象一下股票市场的每日波动，天气模式的周期性变化，甚至细胞分裂的随机性。这些都不是静止的状态，而是由一系列相互影响的随机事件构成的动态过程。《随机漫步的宇宙》将带领读者领略，如何通过数学模型来捕捉和分析这些动态过程。我们将介绍“马尔可夫链”这一强大的工具，它能够描述系统在不同状态之间进行随机转移的可能性，从而预测系统的长期演变趋势。例如，我们可以利用马尔可夫链来模拟一个城市的交通流量，预测其在不同时段的拥堵情况；或者，我们可以用它来理解基因在代际间的传递，预测特定基因的流行度。 “大数定律”和“中心极限定理”是概率论中两颗璀璨的明珠，它们揭示了在大量重复实验中，随机性如何逐渐趋向于规律性。我们将用生动有趣的例子，阐释这两个定理的深刻含义。想象一下，你随机抽取一份报纸，其中某个词语出现的频率可能与全球平均频率相差甚远。但如果你随机抽取成千上万份报纸，那么这个词语的平均出现频率，将无限接近于理论上的真实概率。这就是大数定律的力量。而中心极限定理则告诉我们，即使原始数据的分布形态各异，多次独立抽样的平均值，其分布也将趋向于正态分布（高斯分布），这解释了为何自然界中许多现象都呈现出钟形曲线的特征，例如测量误差、身高分布等等。 本书还将触及“信息论”与“随机性”的交织。信息的本质，往往在于其“意外性”或“不确定性”。一个完全可以预测的消息，其信息量微乎其微。相反，一个完全出乎意料的事件，却蕴含着丰富的信息。我们将探讨熵（entropy）的概念，它不仅是物理学中衡量混乱程度的指标，更是信息论中衡量不确定性程度的度量。通过理解熵，我们可以更深入地认识信息是如何被编码、传输和解码的，以及噪声（随机干扰）在信息传播过程中扮演的角色。 “混沌理论”将为我们的探索增添一抹令人着迷的色彩。在看似随机的系统中，我们有时会发现隐藏的秩序，而微小的初始差异，却可能导致完全不同的结果，这就是所谓的“蝴蝶效应”。我们将探讨如何利用分形几何等数学工具，来描述和理解这些混沌系统的行为。例如，海岸线的长度究竟是多少？答案取决于我们测量的方式，而海岸线本身具有无限的细节，这正是分形几何的体现。混沌系统并非完全随机，而是遵循着 deterministic（确定性）的规律，但由于其对初始条件的极度敏感，使得长期预测变得不可能。 本书的篇幅还将涉及“统计推断”这一重要领域。在拥有有限的样本数据时，我们如何对整体群体进行合理的推测？例如，在一项民意调查中，我们通过采访一部分选民来预测全体选民的投票倾向。统计推断的方法，如置信区间和假设检验，正是帮助我们在不确定性中做出明智判断的工具。我们将揭示其背后的逻辑，理解统计显著性与实际意义的区别，以及抽样误差如何影响我们的推论。 在探索数学模型的同时，本书还将穿插大量引人入胜的真实世界案例。我们将审视自然界的奇妙现象：从病毒的传播模型，到生态系统中物种数量的动态变化；从天体运行的轨道概率，到量子力学中微观粒子的不确定性。我们也将考察人类社会的运作：从金融市场的风险评估，到人工智能的决策过程；从社会网络的演化，到疾病的流行病学研究。这些案例将生动地说明，概率的思维方式，已渗透到现代科学和技术的方方面面，成为我们理解和改造世界不可或缺的工具。 《随机漫步的宇宙》最终旨在唤醒读者对“可能性”的敬畏，对“偶然”的欣赏，以及对“规律”的探求。它将展示，即使在看似混乱无序的世界中，也存在着深刻的数学之美和内在的逻辑。通过理解随机性的力量，我们能够更好地应对生活中的不确定性，做出更明智的决策，并以一种全新的视角，去观察和理解我们所处的这个既充满秩序又蕴藏无限可能性的宇宙。这本书是一扇通往更深层次理解的大门，它邀请您一同漫步于概率的星空，感受数学的魅力，沉思随机性带给我们的启示。
作者简介
目录信息
PartⅠ Principlesandelementaryapplications
1 Plausiblereasoning
1.1 Deductiveandplausiblereasoning
1.2 Analogieswith slcaltheories
1.3 Thethinkingcomputer
1.4 Introducingtherobot
1.5 Booleanalgebra
1.6 Adequatesetsofoperations
1.7 Thebasicdesiderata
1.8 Comments
1.8.1 Commonlanguagevs.formallogic
1.8.2 Nitpicking
2 Thequantitativerules
2.1 Theproductrule
2.2 Thesumrule
2.3 Qualitativeproperties
2.4 Numericalvalues
2.5 Notationandfinite-setspolicy
2.6 Comments
2.6.1 Suectlvevs.oectlve
2.6.2 G/3delstheorem
2.6.3 Venndiagrams
2.6.4 TheKolmogorovaxioms
3 Elementarysamplingtheory
3.1 Samplingwithoutreplacement
3.2 Logicvs.propensity
3.3 Reasoningfromlesspreciseinformation
3.4 Expectations
3.5 Otherformsandextensions
3.6 Probabilityasamathematicaltool
3.7 Thebinomialdistribution
3.8 Samplingwithreplacement
3.8.1 Digression：asermononrealityvs.models
3.9 Correctionforcorrelations
3.10 Simplification
3.11 Comments
3.11.1 Alookahead
4 Elementaryhypothesistesting
4.1 Priorprobabilities
4.2 Testingbinaryhypotheseswithbinarydata
4.3 Nonextensibilitybeyondthebinarycase
4.4 Multiplehypothesistesting
4.4.1 Digressiononanotherderivation
4.5 Continuousprobabilitydistributionfunctions
4.6 Testinganinfinitenumberofhypotheses
4.6.1 Historicaldigression
4.7 Simpleandcompound(orcomposite)hypotheses
4.8 Comments
4.8.1 Etymology
4.8.2 Whathaveweaccomplished?
5 Queerusesforprobabilitytheory
5.1 Extrasensoryperception
5.2 MrsStewartstelepathicpowers
5.2.1 Digressiononthenormalapproximation
5.2.2 BacktoMrsStewart
5.3 Converginganddivergingviews
5.4 Visualperception-evolutionintoBayesianity?
5.5 ThediscoveryofNeptune
5.5.1 Digressiononalternativehypotheses
5.5.2 BacktoNewton
5.6 Horseracingandweatherforecasting
5.6.1 Discussion
5.7 Paradoxesofintuition
5.8 Bayesianjurisprudence
5.9 Comments
5.9.1 Whatisqueer?
6 Elementaryparameterestimation
6.1 Inversionoftheumdistributions
6.2 BothNandRunknown
6.3 Uniformprior
6.4 Predictivedistributions
6.5 Truncateduniformpriors
6.6 Aconcaveprior
6.7 Thebinomialmonkeyprior
6.8 Metamorphosisintocontinuousparameterestimation
6.9 Estimationwithabinomialsamplingdistribution
6.9.1 Digressiononoptionalstopping
6.10 Compoundestimationproblems
6.11 AsimpleBayesianestimate：quantitativepriorinformation
6.11.1 Fromposteriordistributionfunctiontoestimate
6.12 Effectsofqualitativepriorinformation
6.13 Choiceofaprior
6.14 Onwiththecalculation!
6.15 TheJeffreysprior
6.16 Thepointofitall
6.17 Intervalestimation
6.18 Calculationofvariance
6.19 Generalizationandasymptoticforms
6.20 Rectangularsamplingdistribution
6.21 Smallsamples
6.22 Mathematicaltrickery
6.23 Comments
7 Thecentral，Gaussianornormaldistribution
7.1 Thegravitatingphenomenon
7.2 TheHerschel-Maxwellderivation
7.3 TheGaussderivation
7.4 HistoricalimportanceofGausssresult
7.5 TheLandonderivation
7.6 WhytheubiquitoususeofGausslandistributions?
7.7 Whytheubiquitoussuccess?
7.8 Whatestimatorshouldweuse?
7.9 Errorcancellation
7.10 Thenearirrelevanceofsamplingfrequencydistributions
7.11 Theremarkableefficiencyofinformationtransfer
7.12 Othersamplingdistributions
7.13 Nuisanceparametersassafetydevices
7.14 Moregeneralproperties
7.15 ConvolutionofGaussians
7.16 Thecentrallimittheorem
7.17 Accuracyofcomputations
7.18 Galtonsdiscovery
7.19 PopulationdynamicsandDarwinianevolution
7.20 Evolutionofhumming-birdsandflowers
7.21 Applicationtoeconomics
7.22 ThegreatinequalityofJupiterandSaturn
7.23 ResolutionofdistributionsintoGaussians
7.24 Hermitepolynomialsolutions
7.25 Fouriertransformrelations
7.26 Thereishopeafterall
7.27 Comments
7.27.1 Terminologyagain
8 Sufficiency，ancillarity，andallthat
8.1 Sufficiency
8.2 Fishersufficiency
8.2.1 Examples
8.2.2 TheBlackwell-Raotheorem
8.3 Generalizedsufficiency
8.4 Sufficiencyplusnuisanceparameters
8.5 Thelikelihoodprinciple
8.6 Ancillarity
8.7 Generalizedancillaryinformation
8.8 Asymptoticlikelihood：Fisherinformation
8.9 Combiningevidencefromdifferentsources
8.10 Poolingthedata
8.10.1 Fine-grainedpropositions
8.11 Samsbrokenthermometer
8.12 Comments
8.12.1 Thefallacyofsamplere-use
8.12.2 Afolktheorem
8.12.3 Effectofpriorinformation
8.12.4 Clevertricksandgamesmanship
9 Repetitiveexperiments：probabilityandfrequency
9.1 Physicalexperiments
9.2 Thepoorlyinformedrobot
9.3 Induction
9.4 Aretheregeneralinductiverules?
9.5 Multiplicityfactors
9.6 Partitionfunctionalgorithms
9.6.1 Solutionbyinspection
9.7 Entropyalgorithms
9.8 Anotherwayoflookingatit
9.9 Entropymaximization
9.10 Probabilityandfrequency
9.11 Significancetests
9.11.1 Impliedalternatives
9.12 Comparisonofpsiandchi-squared
9.13 Thechi-squaredtest
9.14 Generalization
9.15 Halleysmortalitytable
9.16 Comments
9.16.1 Theirrationalists
9.16.2 Superstitions
10 Physicsofrandomexperiments
10.1 Aninterestingcorrelation
10.2 Historicalbackground
10.3 Howtocheatatcoinanddietossing
10.3.1 Experimentalevidence
10.4 Bridgehands
10.5 Generalrandomexperiments
10.6 Inductionrevisited
10.7 Butwhataboutquantumtheory?
10.8 Mechanicsundertheclouds
10.9 Moreoncoinsandsymmetry
10.10 Independenceoftosses
10.11 Thearroganceoftheuninformed
PartⅡ Advancedapplications
11 Discretepriorprobabilities：theentropyprinciple
11.1 Anewkindofpriorinformation
11.2 Minimum∑Pi2
11.3 Entropy：Shannonstheorem
11.4 TheWallisderivation
11.5 Anexample
11.6 Generalization：amorerigorousproof
11.7 Formalpropertiesofmaximumentropydistributions
11.8 Conceptualproblems-frequencycorrespondence
11.9 Comments
12 Ignorancepriorsandtransformationgroups
12.1 Whatarewetryingtodo?
12.2 Ignorancepriors
12.3 Continuousdistributions
12.4 Transformationgroups
12.4.1 Locationandscaleparameters
12.4.2 APoissonrate
12.4.3 Unknownprobabilityforsuccess
12.4.4 Bertrandsproblem
12.5 Comments
13 Decisiontheory，historicalbackground
13.1 Inferencevs.decision
13.2 DanielBernoullissuggestion
13.3 Therationaleofinsurance
13.4 Entropyandutility
13.5 Thehonestweatherman
13.6 ReactionstoDanielBernoulliandLaplace
13.7 Waldsdecisiontheory
13.8 Parameterestimationforminimumloss
13.9 Reformulationoftheproblem
13.10 Effectofvaryinglossfunctions
13.11 Generaldecisiontheory
13.12 Comments
13.12.1 Objectivityofdecisiontheory
13.12.2 Lossfunctionsinhumansociety
13.12.3 AnewlookattheJeffreysprior
13.12.4 Decisiontheoryisnotfundamental
13.12.5 Anotherdimension?
14 Simpleapplicationsofdecisiontheory
14.1 Definitionsandpreliminaries
14.2 Sufficiencyandinformation
14.3 Lossfunctionsandcriteriaofoptimumperformance
14.4 Adiscreteexample
14.5 Howwouldourrobotdoit?
14.6 Historicalremarks
14.6.1 Theclassicalmatchedfilter
14.7 Thewidgetproblem
14.7.1 SolutionforStage2
14.7.2 SolutionforStage3
14.7.3 SolutionforStage4
14.8 Comments
15 Paradoxesofprobabilitytheory
15.1 Howdoparadoxessurviveandgrow?
15.2 Summingaseriestheeasyway
15.3 Nonconglomerability
15.4 Thetumblingtetrahedra
15.5 Solutionforafinitenumberoftosses
15.6 Finitevs.countableadditivity
15.7 TheBorel-Kolmogorovparadox
15.8 Themarginalizationparadox
15.8.1 Ontogreaterdisasters
15.9 Discussion
15.9.1 TheDSZExample#5
15.9.2 Summary
15.10 Ausefulresultafterall?
15.11 Howtomass-produceparadoxes
15.12 Comments
16 Orthodoxmethods：historicalbackground
16.1 Theearlyproblems
16.2 Sociologyoforthodoxstatistics
16.3 RonaldFisher，HaroldJeffreys，andJerzyNeyman
16.4 Pre-dataandpost-dataconsiderations
16.5 Thesamplingdistributionforanestimator
16.6 Pro-causalandanti-causalbias
16.7 Whatisreal，theprobabilityorthephenomenon?
16.8 Comments
16.8.1 Communicationdifficulties
17 Principlesandpathologyoforthodoxstatistics
17.1 Informationloss
17.2 Unbiasedestimators
17.3 Pathologyofanunbiasedestimate
17.4 Thefundamentalinequalityofthesamplingvariance
17.5 Periodicity：theweatherinCentralPark
17.5.1 Thefollyofpre-filteringdata
17.6. ABayesiananalysis
17.7 Thefollyofrandomization
17.8 Fisher：commonsenseatRothamsted
17.8.1 TheBayesiansafetydevice
17.9 Missingdata
17.10 Trendandseasonalityintimeseries
17.10.1 Orthodoxmethods
17.10.2 TheBayesianmethod
17.10.3 ComparisonofBayesianandorthodoxestimates
17.10.4 Animprovedorthodoxestimate
17.10.5 Theorthodoxcriterionofperformance
17.11 Thegeneralcase
17.12 Comments
18 TheApdistributionandruleofsuccession
18.1 Memorystorageforoldrobots
18.2 Relevance
18.3 Asurprisingconsequence
18.4 Outerandinnerrobots
18.5 Anapplication
18.6 Laplacesruleofsuccession
18.7 Jeffreysobjection
18.8 Bassorcarp?
18.9 Sowheredoesthisleavetherule?
18.10 Generalization
18.11 Confirmationandweightofevidence
18.11.1 Isindifferencebasedonknowledgeorignorance?
18.12 Camapsinductivemethods
18.13 Probabilityandfrequencyinexchangeablesequences
18.14 Predictionoffrequencies
18.15 One-dimensionalneutronmultiplication
18.15.1 Thefrequentistsolution
18.15.2 TheLaplacesolution
18.16 ThedeFinettitheorem
18.17 Comments
19 Physicalmeasurements
19.1 Reductionofequationsofcondition
19.2 Reformulationasadecisionproblem
19.2.1 SermononGaussianerrordistributions
19.3 Theunderdeterminedcase：Kissingular
19.4 Theoverdeterminedcase：Kcanbemadenonsingular
19.5 Numericalevaluationoftheresult
19.6 Accuracyoftheestimates
19.7 Comments
19.7.1 Aparadox
20 Modelcomparison
20.1 Formulationoftheproblem
20.2 Thefairjudgeandthecruelrealist
20.2.1 Parametersknowninadvance
20.2.2 Parametersunknown
20.3 Butwhereistheideaofsimplicity?
20.4 Anexample：linearresponsemodels
20.4.1 Digression：theoldsermonstillanothertime
20.5 Comments
20.5.1 Finalcauses
21 Outliersandrobustness
21.1 Theexperimentersdilemma
21.2 Robustness
21.3 Thetwo-modelmodel
21.4 Exchangeableselection
21.5 ThegeneralBayesiansolution
21.6 Pureoutliers
21.7 Onerecedingdatum
22 Introductiontocommunicationtheory
22.1 Originsofthetheory
22.2 Thenoiselesschannel
22.3 Theinformationsource
22.4 DoestheEnglishlanguagehavestatisticalproperties?
22.5 Optimumencoding：letterfrequenciesknown
22.6 Betterencodingfromknowledgeofdigramfrequencies
22.7 Relationtoastochasticmodel
22.8 Thenoisychannel
AppendixA Otherapproachestoprobabilitytheory
A.1 TheKolmogorovsystemofprobability
A.2 ThedeFinettisystemofprobability
A.3 Comparativeprobability
A.4 Holdoutsagainstuniversalcomparability
A.5 Speculationsaboutlatticetheories
AppendixB Mathematicalformalitiesandstyle
B.1 Notationandlogicalhierarchy
B.2 Ourcautiousapproachpolicy
B.3 WillyFelleronmeasuretheory
B.4 Kroneckervs.Weierstrasz
B.5 Whatisalegitimatemathematicalfunction?
B.5.1 Delta-functions
B.5.2 Nondifferentiablefunctions
B.5.3 Bogusnondifferentiablefunctions
B.6 Countinginfinitesets?
B.7 TheHausdorffsphereparadoxandmathematicaldiseases
B.8 WhatamIsupposedtopublish?
B.9 Mathematicalcourtesy
AppendixC Convolutionsandcumulants
C.1 Relationofcumulantsandmoments
· · · · · · (收起)
1 Plausiblereasoning
1.1 Deductiveandplausiblereasoning
1.2 Analogieswith slcaltheories
1.3 Thethinkingcomputer
1.4 Introducingtherobot
1.5 Booleanalgebra
1.6 Adequatesetsofoperations
1.7 Thebasicdesiderata
1.8 Comments
1.8.1 Commonlanguagevs.formallogic
1.8.2 Nitpicking
2 Thequantitativerules
2.1 Theproductrule
2.2 Thesumrule
2.3 Qualitativeproperties
2.4 Numericalvalues
2.5 Notationandfinite-setspolicy
2.6 Comments
2.6.1 Suectlvevs.oectlve
2.6.2 G/3delstheorem
2.6.3 Venndiagrams
2.6.4 TheKolmogorovaxioms
3 Elementarysamplingtheory
3.1 Samplingwithoutreplacement
3.2 Logicvs.propensity
3.3 Reasoningfromlesspreciseinformation
3.4 Expectations
3.5 Otherformsandextensions
3.6 Probabilityasamathematicaltool
3.7 Thebinomialdistribution
3.8 Samplingwithreplacement
3.8.1 Digression：asermononrealityvs.models
3.9 Correctionforcorrelations
3.10 Simplification
3.11 Comments
3.11.1 Alookahead
4 Elementaryhypothesistesting
4.1 Priorprobabilities
4.2 Testingbinaryhypotheseswithbinarydata
4.3 Nonextensibilitybeyondthebinarycase
4.4 Multiplehypothesistesting
4.4.1 Digressiononanotherderivation
4.5 Continuousprobabilitydistributionfunctions
4.6 Testinganinfinitenumberofhypotheses
4.6.1 Historicaldigression
4.7 Simpleandcompound(orcomposite)hypotheses
4.8 Comments
4.8.1 Etymology
4.8.2 Whathaveweaccomplished?
5 Queerusesforprobabilitytheory
5.1 Extrasensoryperception
5.2 MrsStewartstelepathicpowers
5.2.1 Digressiononthenormalapproximation
5.2.2 BacktoMrsStewart
5.3 Converginganddivergingviews
5.4 Visualperception-evolutionintoBayesianity?
5.5 ThediscoveryofNeptune
5.5.1 Digressiononalternativehypotheses
5.5.2 BacktoNewton
5.6 Horseracingandweatherforecasting
5.6.1 Discussion
5.7 Paradoxesofintuition
5.8 Bayesianjurisprudence
5.9 Comments
5.9.1 Whatisqueer?
6 Elementaryparameterestimation
6.1 Inversionoftheumdistributions
6.2 BothNandRunknown
6.3 Uniformprior
6.4 Predictivedistributions
6.5 Truncateduniformpriors
6.6 Aconcaveprior
6.7 Thebinomialmonkeyprior
6.8 Metamorphosisintocontinuousparameterestimation
6.9 Estimationwithabinomialsamplingdistribution
6.9.1 Digressiononoptionalstopping
6.10 Compoundestimationproblems
6.11 AsimpleBayesianestimate：quantitativepriorinformation
6.11.1 Fromposteriordistributionfunctiontoestimate
6.12 Effectsofqualitativepriorinformation
6.13 Choiceofaprior
6.14 Onwiththecalculation!
6.15 TheJeffreysprior
6.16 Thepointofitall
6.17 Intervalestimation
6.18 Calculationofvariance
6.19 Generalizationandasymptoticforms
6.20 Rectangularsamplingdistribution
6.21 Smallsamples
6.22 Mathematicaltrickery
6.23 Comments
7 Thecentral，Gaussianornormaldistribution
7.1 Thegravitatingphenomenon
7.2 TheHerschel-Maxwellderivation
7.3 TheGaussderivation
7.4 HistoricalimportanceofGausssresult
7.5 TheLandonderivation
7.6 WhytheubiquitoususeofGausslandistributions?
7.7 Whytheubiquitoussuccess?
7.8 Whatestimatorshouldweuse?
7.9 Errorcancellation
7.10 Thenearirrelevanceofsamplingfrequencydistributions
7.11 Theremarkableefficiencyofinformationtransfer
7.12 Othersamplingdistributions
7.13 Nuisanceparametersassafetydevices
7.14 Moregeneralproperties
7.15 ConvolutionofGaussians
7.16 Thecentrallimittheorem
7.17 Accuracyofcomputations
7.18 Galtonsdiscovery
7.19 PopulationdynamicsandDarwinianevolution
7.20 Evolutionofhumming-birdsandflowers
7.21 Applicationtoeconomics
7.22 ThegreatinequalityofJupiterandSaturn
7.23 ResolutionofdistributionsintoGaussians
7.24 Hermitepolynomialsolutions
7.25 Fouriertransformrelations
7.26 Thereishopeafterall
7.27 Comments
7.27.1 Terminologyagain
8 Sufficiency，ancillarity，andallthat
8.1 Sufficiency
8.2 Fishersufficiency
8.2.1 Examples
8.2.2 TheBlackwell-Raotheorem
8.3 Generalizedsufficiency
8.4 Sufficiencyplusnuisanceparameters
8.5 Thelikelihoodprinciple
8.6 Ancillarity
8.7 Generalizedancillaryinformation
8.8 Asymptoticlikelihood：Fisherinformation
8.9 Combiningevidencefromdifferentsources
8.10 Poolingthedata
8.10.1 Fine-grainedpropositions
8.11 Samsbrokenthermometer
8.12 Comments
8.12.1 Thefallacyofsamplere-use
8.12.2 Afolktheorem
8.12.3 Effectofpriorinformation
8.12.4 Clevertricksandgamesmanship
9 Repetitiveexperiments：probabilityandfrequency
9.1 Physicalexperiments
9.2 Thepoorlyinformedrobot
9.3 Induction
9.4 Aretheregeneralinductiverules?
9.5 Multiplicityfactors
9.6 Partitionfunctionalgorithms
9.6.1 Solutionbyinspection
9.7 Entropyalgorithms
9.8 Anotherwayoflookingatit
9.9 Entropymaximization
9.10 Probabilityandfrequency
9.11 Significancetests
9.11.1 Impliedalternatives
9.12 Comparisonofpsiandchi-squared
9.13 Thechi-squaredtest
9.14 Generalization
9.15 Halleysmortalitytable
9.16 Comments
9.16.1 Theirrationalists
9.16.2 Superstitions
10 Physicsofrandomexperiments
10.1 Aninterestingcorrelation
10.2 Historicalbackground
10.3 Howtocheatatcoinanddietossing
10.3.1 Experimentalevidence
10.4 Bridgehands
10.5 Generalrandomexperiments
10.6 Inductionrevisited
10.7 Butwhataboutquantumtheory?
10.8 Mechanicsundertheclouds
10.9 Moreoncoinsandsymmetry
10.10 Independenceoftosses
10.11 Thearroganceoftheuninformed
PartⅡ Advancedapplications
11 Discretepriorprobabilities：theentropyprinciple
11.1 Anewkindofpriorinformation
11.2 Minimum∑Pi2
11.3 Entropy：Shannonstheorem
11.4 TheWallisderivation
11.5 Anexample
11.6 Generalization：amorerigorousproof
11.7 Formalpropertiesofmaximumentropydistributions
11.8 Conceptualproblems-frequencycorrespondence
11.9 Comments
12 Ignorancepriorsandtransformationgroups
12.1 Whatarewetryingtodo?
12.2 Ignorancepriors
12.3 Continuousdistributions
12.4 Transformationgroups
12.4.1 Locationandscaleparameters
12.4.2 APoissonrate
12.4.3 Unknownprobabilityforsuccess
12.4.4 Bertrandsproblem
12.5 Comments
13 Decisiontheory，historicalbackground
13.1 Inferencevs.decision
13.2 DanielBernoullissuggestion
13.3 Therationaleofinsurance
13.4 Entropyandutility
13.5 Thehonestweatherman
13.6 ReactionstoDanielBernoulliandLaplace
13.7 Waldsdecisiontheory
13.8 Parameterestimationforminimumloss
13.9 Reformulationoftheproblem
13.10 Effectofvaryinglossfunctions
13.11 Generaldecisiontheory
13.12 Comments
13.12.1 Objectivityofdecisiontheory
13.12.2 Lossfunctionsinhumansociety
13.12.3 AnewlookattheJeffreysprior
13.12.4 Decisiontheoryisnotfundamental
13.12.5 Anotherdimension?
14 Simpleapplicationsofdecisiontheory
14.1 Definitionsandpreliminaries
14.2 Sufficiencyandinformation
14.3 Lossfunctionsandcriteriaofoptimumperformance
14.4 Adiscreteexample
14.5 Howwouldourrobotdoit?
14.6 Historicalremarks
14.6.1 Theclassicalmatchedfilter
14.7 Thewidgetproblem
14.7.1 SolutionforStage2
14.7.2 SolutionforStage3
14.7.3 SolutionforStage4
14.8 Comments
15 Paradoxesofprobabilitytheory
15.1 Howdoparadoxessurviveandgrow?
15.2 Summingaseriestheeasyway
15.3 Nonconglomerability
15.4 Thetumblingtetrahedra
15.5 Solutionforafinitenumberoftosses
15.6 Finitevs.countableadditivity
15.7 TheBorel-Kolmogorovparadox
15.8 Themarginalizationparadox
15.8.1 Ontogreaterdisasters
15.9 Discussion
15.9.1 TheDSZExample#5
15.9.2 Summary
15.10 Ausefulresultafterall?
15.11 Howtomass-produceparadoxes
15.12 Comments
16 Orthodoxmethods：historicalbackground
16.1 Theearlyproblems
16.2 Sociologyoforthodoxstatistics
16.3 RonaldFisher，HaroldJeffreys，andJerzyNeyman
16.4 Pre-dataandpost-dataconsiderations
16.5 Thesamplingdistributionforanestimator
16.6 Pro-causalandanti-causalbias
16.7 Whatisreal，theprobabilityorthephenomenon?
16.8 Comments
16.8.1 Communicationdifficulties
17 Principlesandpathologyoforthodoxstatistics
17.1 Informationloss
17.2 Unbiasedestimators
17.3 Pathologyofanunbiasedestimate
17.4 Thefundamentalinequalityofthesamplingvariance
17.5 Periodicity：theweatherinCentralPark
17.5.1 Thefollyofpre-filteringdata
17.6. ABayesiananalysis
17.7 Thefollyofrandomization
17.8 Fisher：commonsenseatRothamsted
17.8.1 TheBayesiansafetydevice
17.9 Missingdata
17.10 Trendandseasonalityintimeseries
17.10.1 Orthodoxmethods
17.10.2 TheBayesianmethod
17.10.3 ComparisonofBayesianandorthodoxestimates
17.10.4 Animprovedorthodoxestimate
17.10.5 Theorthodoxcriterionofperformance
17.11 Thegeneralcase
17.12 Comments
18 TheApdistributionandruleofsuccession
18.1 Memorystorageforoldrobots
18.2 Relevance
18.3 Asurprisingconsequence
18.4 Outerandinnerrobots
18.5 Anapplication
18.6 Laplacesruleofsuccession
18.7 Jeffreysobjection
18.8 Bassorcarp?
18.9 Sowheredoesthisleavetherule?
18.10 Generalization
18.11 Confirmationandweightofevidence
18.11.1 Isindifferencebasedonknowledgeorignorance?
18.12 Camapsinductivemethods
18.13 Probabilityandfrequencyinexchangeablesequences
18.14 Predictionoffrequencies
18.15 One-dimensionalneutronmultiplication
18.15.1 Thefrequentistsolution
18.15.2 TheLaplacesolution
18.16 ThedeFinettitheorem
18.17 Comments
19 Physicalmeasurements
19.1 Reductionofequationsofcondition
19.2 Reformulationasadecisionproblem
19.2.1 SermononGaussianerrordistributions
19.3 Theunderdeterminedcase：Kissingular
19.4 Theoverdeterminedcase：Kcanbemadenonsingular
19.5 Numericalevaluationoftheresult
19.6 Accuracyoftheestimates
19.7 Comments
19.7.1 Aparadox
20 Modelcomparison
20.1 Formulationoftheproblem
20.2 Thefairjudgeandthecruelrealist
20.2.1 Parametersknowninadvance
20.2.2 Parametersunknown
20.3 Butwhereistheideaofsimplicity?
20.4 Anexample：linearresponsemodels
20.4.1 Digression：theoldsermonstillanothertime
20.5 Comments
20.5.1 Finalcauses
21 Outliersandrobustness
21.1 Theexperimentersdilemma
21.2 Robustness
21.3 Thetwo-modelmodel
21.4 Exchangeableselection
21.5 ThegeneralBayesiansolution
21.6 Pureoutliers
21.7 Onerecedingdatum
22 Introductiontocommunicationtheory
22.1 Originsofthetheory
22.2 Thenoiselesschannel
22.3 Theinformationsource
22.4 DoestheEnglishlanguagehavestatisticalproperties?
22.5 Optimumencoding：letterfrequenciesknown
22.6 Betterencodingfromknowledgeofdigramfrequencies
22.7 Relationtoastochasticmodel
22.8 Thenoisychannel
AppendixA Otherapproachestoprobabilitytheory
A.1 TheKolmogorovsystemofprobability
A.2 ThedeFinettisystemofprobability
A.3 Comparativeprobability
A.4 Holdoutsagainstuniversalcomparability
A.5 Speculationsaboutlatticetheories
AppendixB Mathematicalformalitiesandstyle
B.1 Notationandlogicalhierarchy
B.2 Ourcautiousapproachpolicy
B.3 WillyFelleronmeasuretheory
B.4 Kroneckervs.Weierstrasz
B.5 Whatisalegitimatemathematicalfunction?
B.5.1 Delta-functions
B.5.2 Nondifferentiablefunctions
B.5.3 Bogusnondifferentiablefunctions
B.6 Countinginfinitesets?
B.7 TheHausdorffsphereparadoxandmathematicaldiseases
B.8 WhatamIsupposedtopublish?
B.9 Mathematicalcourtesy
AppendixC Convolutionsandcumulants
C.1 Relationofcumulantsandmoments
· · · · · · (收起)
读后感
现在回过头来再看看这本书的前言，只能说，庆幸自己能看到 E. T. Jaynes 的这本了用半个世纪完成的著作。因为就在几年前的概率论课上我学的还是那种由一些基本的奇怪的论述构建起的令人十分不安的理论，比如说扔一个均匀硬币头朝上的概率是二分之一（你要证实这一点只要扔无数...
现在回过头来再看看这本书的前言，只能说，庆幸自己能看到 E. T. Jaynes 的这本了用半个世纪完成的著作。因为就在几年前的概率论课上我学的还是那种由一些基本的奇怪的论述构建起的令人十分不安的理论，比如说扔一个均匀硬币头朝上的概率是二分之一（你要证实这一点只要扔无数...
现在回过头来再看看这本书的前言，只能说，庆幸自己能看到 E. T. Jaynes 的这本了用半个世纪完成的著作。因为就在几年前的概率论课上我学的还是那种由一些基本的奇怪的论述构建起的令人十分不安的理论，比如说扔一个均匀硬币头朝上的概率是二分之一（你要证实这一点只要扔无数...
Probability theory as extended logic. ##preface ### comparisons The author violently slashes frequentist statistics. Bayesian analysis is kinda speculative, amouting to expressing some prior knowledge or working hypothesis, while Maximum Entropy method is n...
Probability theory as extended logic. ##preface ### comparisons The author violently slashes frequentist statistics. Bayesian analysis is kinda speculative, amouting to expressing some prior knowledge or working hypothesis, while Maximum Entropy method is n...
用户评价
说真的，我很久没读过这么“有味道”的理论书了。这本书的语言风格非常独特，它不像是在写一本严肃的学术专著，更像是一位经验丰富的智者在与你进行一场深入且充满激情的探讨。字里行间透露出作者对概率这门学科深沉的热爱和敬畏。尤其是在探讨大数定律和中心极限定理时，作者的措辞充满了力量感和画面感，让人能够清晰地“看到”那些抽象的极限过程是如何在无数次重复中实现稳定性的。它成功地将数学的严谨与人文的温度结合起来，让晦涩的证明过程也变得引人入胜。对于我这样需要将概率理论应用于复杂系统分析的人来说，这本书提供的不仅仅是知识，更是一种看待问题、解决问题的全新视角和精神激励。
这本书的魅力在于它的“厚度”和“广度”的完美结合。它没有满足于停留在教科书的层面，而是勇敢地触及了许多前沿且富有争议性的概率应用领域。作者在介绍基础理论的同时，还穿插了大量精彩的历史典故和科学史上的关键转折点，这使得原本冰冷的数学知识变得有血有肉，充满了人性的挣扎与智慧的光芒。我特别喜欢它在论述统计推断的局限性时所展现出的那种坦诚和批判精神，这在很多同类书籍中是少见的。它鼓励读者保持怀疑，警惕过度依赖模型的陷阱，这对于培养真正的科学素养至关重要。读完后，我感觉自己对世界运作的随机性有了更成熟、更负责任的认知。
这本书真是让人大开眼界，它不仅仅是简单地堆砌公式和定理，更像是一场深入人心的哲学对话。作者的笔触细腻而富有洞察力，将那些原本晦涩难懂的概率概念，通过生动的例子和精妙的比喻，层层剥开，展现出它们背后蕴含的深刻逻辑。阅读过程中，我仿佛被带入了一个由不确定性构建的宏大世界，每一个概率事件都充满了偶然的美感和必然的规律。作者擅长引导读者去思考“为什么会这样”，而不是仅仅停留在“是什么”的层面。这种深入骨髓的探讨，让人在掌握知识的同时，也能感受到思维被拓展的愉悦。它不是那种读完就忘的工具书，而是一本值得反复咀嚼，每次都能品出新意的佳作。我尤其欣赏其中对于随机过程的描述，那种对时间流逝中事件演变的把握，充满了诗意和科学的严谨性。
说实话，我一开始有点担心内容会过于学术化，毕竟概率论这个领域听起来就挺让人头疼的。但这本书完全出乎我的意料，它的叙述方式极其流畅，读起来毫不费力，仿佛在听一位睿智的长者娓娓道来。作者对于如何构建一个可靠的概率模型有着独到的见解，他不会急于抛出复杂的数学表达，而是先从直觉和现实场景入手，慢慢引导我们建立起清晰的认知框架。这种循序渐进的教学方法，极大地降低了学习的门槛。尤其是在讲解那些经典的悖论和反直觉的案例时，作者的处理方式既尊重了数学的精确性，又兼顾了读者的理解深度，让人在恍然大悟中加深了对随机性本质的理解。对于那些希望真正理解概率论“灵魂”而非仅仅记忆公式的人来说，这本书无疑是上乘之选。
我一直觉得，好的数学书籍应该具备一种“雕塑感”，这本书就完美地体现了这一点。作者对于每一个概念的阐述都经过了精心的打磨和取舍，没有一丝多余的赘述，却又充分地保证了逻辑链条的完整性。它就像是一件精心制作的艺术品，线条流畅，结构清晰，每一部分都恰到好处地承载着特定的信息和意义。我在阅读一些关于条件概率和贝叶斯推断的部分时，感受到了强烈的结构美学。作者巧妙地将看似分散的知识点编织成一张严密的网，让人清晰地看到不同概率工具之间的内在联系和相互支撑。这本书不仅教会了我如何计算，更重要的是，它教会了我如何“思考”概率问题，如何用一种更结构化、更审慎的态度去面对生活中的不确定性。
一切皆有可能 只是发生概率大小的问题
好好读一下
jayn之后，再无统计
这本书可以写得更加简洁一些。很有物理感。
神作，分析哲学路径的概率论
