概率论沉思录：（英文版）

作者: [美] 杰恩斯（E.T.Jaynes）著

出版社: 人民邮电出版社

出版时间: 2009-04

版次: 1

ISBN: 9787115195364

定价: 99.00

装帧: 平装

开本: 16开

纸张: 胶版纸

页数: 727页

字数: 753千字

正文语种: 英语

丛书: 图灵原版数学·统计学系列

分类: 自然科学

1 张插图图片

139人买过

《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。 E.T.Jaynes（1922—1998）已故著名数学家和物理学家。生前曾任华盛顿大学圣路易斯分校和斯坦福大学教授。他因为提出了热动力学的最大熵原理（1957年）和量子光学的Jaynes-Cummings／模型（1963年）而闻名于世。此后的几十年，他一直在探求将概率和统计推断作为整个科学的逻辑基础这一重大课题，其成果和心得最终凝结为本书。 PartⅠPrinciplesandelementaryapplications
1Plausiblereasoning
1.1Deductiveandplausiblereasoning
1.2Analogieswithslcaltheories
1.3Thethinkingcomputer
1.4Introducingtherobot
1.5Booleanalgebra
1.6Adequatesetsofoperations
1.7Thebasicdesiderata
1.8Comments
1.8.1Commonlanguagevs.formallogic
1.8.2Nitpicking

2Thequantitativerules
2.1Theproductrule
2.2Thesumrule
2.3Qualitativeproperties
2.4Numericalvalues
2.5Notationandfinite-setspolicy
2.6Comments
2.6.1Suectlvevs.oectlve
2.6.2G/3delstheorem
2.6.3Venndiagrams
2.6.4TheKolmogorovaxioms

3Elementarysamplingtheory
3.1Samplingwithoutreplacement
3.2Logicvs.propensity
3.3Reasoningfromlesspreciseinformation
3.4Expectations
3.5Otherformsandextensions
3.6Probabilityasamathematicaltool
3.7Thebinomialdistribution
3.8Samplingwithreplacement
3.8.1Digression：asermononrealityvs.models
3.9Correctionforcorrelations
3.10Simplification
3.11Comments
3.11.1Alookahead

4Elementaryhypothesistesting
4.1Priorprobabilities
4.2Testingbinaryhypotheseswithbinarydata
4.3Nonextensibilitybeyondthebinarycase
4.4Multiplehypothesistesting
4.4.1Digressiononanotherderivation
4.5Continuousprobabilitydistributionfunctions
4.6Testinganinfinitenumberofhypotheses
4.6.1Historicaldigression
4.7Simpleandcompound(orcomposite)hypotheses
4.8Comments
4.8.1Etymology
4.8.2Whathaveweaccomplished?

5Queerusesforprobabilitytheory
5.1Extrasensoryperception
5.2MrsStewartstelepathicpowers
5.2.1Digressiononthenormalapproximation
5.2.2BacktoMrsStewart
5.3Converginganddivergingviews
5.4Visualperception-evolutionintoBayesianity?
5.5ThediscoveryofNeptune
5.5.1Digressiononalternativehypotheses
5.5.2BacktoNewton
5.6Horseracingandweatherforecasting
5.6.1Discussion
5.7Paradoxesofintuition
5.8Bayesianjurisprudence
5.9Comments
5.9.1Whatisqueer?

6Elementaryparameterestimation
6.1Inversionoftheumdistributions
6.2BothNandRunknown
6.3Uniformprior
6.4Predictivedistributions
6.5Truncateduniformpriors
6.6Aconcaveprior
6.7Thebinomialmonkeyprior
6.8Metamorphosisintocontinuousparameterestimation
6.9Estimationwithabinomialsamplingdistribution
6.9.1Digressiononoptionalstopping
6.10Compoundestimationproblems
6.11AsimpleBayesianestimate：quantitativepriorinformation
6.11.1Fromposteriordistributionfunctiontoestimate
6.12Effectsofqualitativepriorinformation
6.13Choiceofaprior
6.14Onwiththecalculation!
6.15TheJeffreysprior
6.16Thepointofitall
6.17Intervalestimation
6.18Calculationofvariance
6.19Generalizationandasymptoticforms
6.20Rectangularsamplingdistribution
6.21Smallsamples
6.22Mathematicaltrickery
6.23Comments

7Thecentral，Gaussianornormaldistribution
7.1Thegravitatingphenomenon
7.2TheHerschel-Maxwellderivation
7.3TheGaussderivation
7.4HistoricalimportanceofGausssresult
7.5TheLandonderivation
7.6WhytheubiquitoususeofGausslandistributions?
7.7Whytheubiquitoussuccess?
7.8Whatestimatorshouldweuse?
7.9Errorcancellation
7.10Thenearirrelevanceofsamplingfrequencydistributions
7.11Theremarkableefficiencyofinformationtransfer
7.12Othersamplingdistributions
7.13Nuisanceparametersassafetydevices
7.14Moregeneralproperties
7.15ConvolutionofGaussians
7.16Thecentrallimittheorem
7.17Accuracyofcomputations
7.18Galtonsdiscovery
7.19PopulationdynamicsandDarwinianevolution
7.20Evolutionofhumming-birdsandflowers
7.21Applicationtoeconomics
7.22ThegreatinequalityofJupiterandSaturn
7.23ResolutionofdistributionsintoGaussians
7.24Hermitepolynomialsolutions
7.25Fouriertransformrelations
7.26Thereishopeafterall
7.27Comments
7.27.1Terminologyagain

8Sufficiency，ancillarity，andallthat
8.1Sufficiency
8.2Fishersufficiency
8.2.1Examples
8.2.2TheBlackwell-Raotheorem
8.3Generalizedsufficiency
8.4Sufficiencyplusnuisanceparameters
8.5Thelikelihoodprinciple
8.6Ancillarity
8.7Generalizedancillaryinformation
8.8Asymptoticlikelihood：Fisherinformation
8.9Combiningevidencefromdifferentsources
8.10Poolingthedata
8.10.1Fine-grainedpropositions
8.11Samsbrokenthermometer
8.12Comments
8.12.1Thefallacyofsamplere-use
8.12.2Afolktheorem
8.12.3Effectofpriorinformation
8.12.4Clevertricksandgamesmanship

9Repetitiveexperiments：probabilityandfrequency
9.1Physicalexperiments
9.2Thepoorlyinformedrobot
9.3Induction
9.4Aretheregeneralinductiverules?
9.5Multiplicityfactors
9.6Partitionfunctionalgorithms
9.6.1Solutionbyinspection
9.7Entropyalgorithms
9.8Anotherwayoflookingatit
9.9Entropymaximization
9.10Probabilityandfrequency
9.11Significancetests
9.11.1Impliedalternatives
9.12Comparisonofpsiandchi-squared
9.13Thechi-squaredtest
9.14Generalization
9.15Halleysmortalitytable
9.16Comments
9.16.1Theirrationalists
9.16.2Superstitions
10Physicsofrandomexperiments
10.1Aninterestingcorrelation
10.2Historicalbackground
10.3Howtocheatatcoinanddietossing
10.3.1Experimentalevidence
10.4Bridgehands
10.5Generalrandomexperiments
10.6Inductionrevisited
10.7Butwhataboutquantumtheory?
10.8Mechanicsundertheclouds
10.9Moreoncoinsandsymmetry
10.10Independenceoftosses
10.11Thearroganceoftheuninformed

PartⅡAdvancedapplications
11Discretepriorprobabilities：theentropyprinciple
11.1Anewkindofpriorinformation
11.2Minimum∑Pi2
11.3Entropy：Shannonstheorem
11.4TheWallisderivation
11.5Anexample
11.6Generalization：amorerigorousproof
11.7Formalpropertiesofmaximumentropydistributions
11.8Conceptualproblems-frequencycorrespondence
11.9Comments

12Ignorancepriorsandtransformationgroups
12.1Whatarewetryingtodo?
12.2Ignorancepriors
12.3Continuousdistributions
12.4Transformationgroups
12.4.1Locationandscaleparameters
12.4.2APoissonrate
12.4.3Unknownprobabilityforsuccess
12.4.4Bertrandsproblem
12.5Comments

13Decisiontheory，historicalbackground
13.1Inferencevs.decision
13.2DanielBernoullissuggestion
13.3Therationaleofinsurance
13.4Entropyandutility
13.5Thehonestweatherman
13.6ReactionstoDanielBernoulliandLaplace
13.7Waldsdecisiontheory
13.8Parameterestimationforminimumloss
13.9Reformulationoftheproblem
13.10Effectofvaryinglossfunctions
13.11Generaldecisiontheory
13.12Comments
13.12.1Objectivityofdecisiontheory
13.12.2Lossfunctionsinhumansociety
13.12.3AnewlookattheJeffreysprior
13.12.4Decisiontheoryisnotfundamental
13.12.5Anotherdimension?

14Simpleapplicationsofdecisiontheory
14.1Definitionsandpreliminaries
14.2Sufficiencyandinformation
14.3Lossfunctionsandcriteriaofoptimumperformance
14.4Adiscreteexample
14.5Howwouldourrobotdoit?
14.6Historicalremarks
14.6.1Theclassicalmatchedfilter
14.7Thewidgetproblem
14.7.1SolutionforStage2
14.7.2SolutionforStage3
14.7.3SolutionforStage4
14.8Comments

15Paradoxesofprobabilitytheory
15.1Howdoparadoxessurviveandgrow?
15.2Summingaseriestheeasyway
15.3Nonconglomerability
15.4Thetumblingtetrahedra
15.5Solutionforafinitenumberoftosses
15.6Finitevs.countableadditivity
15.7TheBorel-Kolmogorovparadox
15.8Themarginalizationparadox
15.8.1Ontogreaterdisasters
15.9Discussion
15.9.1TheDSZExample#5
15.9.2Summary
15.10Ausefulresultafterall?
15.11Howtomass-produceparadoxes
15.12Comments

16Orthodoxmethods：historicalbackground
16.1Theearlyproblems
16.2Sociologyoforthodoxstatistics
16.3RonaldFisher，HaroldJeffreys，andJerzyNeyman
16.4Pre-dataandpost-dataconsiderations
16.5Thesamplingdistributionforanestimator
16.6Pro-causalandanti-causalbias
16.7Whatisreal，theprobabilityorthephenomenon?
16.8Comments
16.8.1Communicationdifficulties

17Principlesandpathologyoforthodoxstatistics
17.1Informationloss
17.2Unbiasedestimators
17.3Pathologyofanunbiasedestimate
17.4Thefundamentalinequalityofthesamplingvariance
17.5Periodicity：theweatherinCentralPark
17.5.1Thefollyofpre-filteringdata
17.6.ABayesiananalysis
17.7Thefollyofrandomization
17.8Fisher：commonsenseatRothamsted
17.8.1TheBayesiansafetydevice
17.9Missingdata
17.10Trendandseasonalityintimeseries
17.10.1Orthodoxmethods
17.10.2TheBayesianmethod
17.10.3ComparisonofBayesianandorthodoxestimates
17.10.4Animprovedorthodoxestimate
17.10.5Theorthodoxcriterionofperformance
17.11Thegeneralcase
17.12Comments

18TheApdistributionandruleofsuccession
18.1Memorystorageforoldrobots
18.2Relevance
18.3Asurprisingconsequence
18.4Outerandinnerrobots
18.5Anapplication
18.6Laplacesruleofsuccession
18.7Jeffreysobjection
18.8Bassorcarp?
18.9Sowheredoesthisleavetherule?
18.10Generalization
18.11Confirmationandweightofevidence
18.11.1Isindifferencebasedonknowledgeorignorance?
18.12Camapsinductivemethods
18.13Probabilityandfrequencyinexchangeablesequences
18.14Predictionoffrequencies
18.15One-dimensionalneutronmultiplication
18.15.1Thefrequentistsolution
18.15.2TheLaplacesolution
18.16ThedeFinettitheorem
18.17Comments

19Physicalmeasurements
19.1Reductionofequationsofcondition
19.2Reformulationasadecisionproblem
19.2.1SermononGaussianerrordistributions
19.3Theunderdeterminedcase：Kissingular
19.4Theoverdeterminedcase：Kcanbemadenonsingular
19.5Numericalevaluationoftheresult
19.6Accuracyoftheestimates
19.7Comments
19.7.1Aparadox

20Modelcomparison
20.1Formulationoftheproblem
20.2Thefairjudgeandthecruelrealist
20.2.1Parametersknowninadvance
20.2.2Parametersunknown
20.3Butwhereistheideaofsimplicity?
20.4Anexample：linearresponsemodels
20.4.1Digression：theoldsermonstillanothertime
20.5Comments
20.5.1Finalcauses

21Outliersandrobustness
21.1Theexperimentersdilemma
21.2Robustness
21.3Thetwo-modelmodel
21.4Exchangeableselection
21.5ThegeneralBayesiansolution
21.6Pureoutliers
21.7Onerecedingdatum

22Introductiontocommunicationtheory
22.1Originsofthetheory
22.2Thenoiselesschannel
22.3Theinformationsource
22.4DoestheEnglishlanguagehavestatisticalproperties?
22.5Optimumencoding：letterfrequenciesknown
22.6Betterencodingfromknowledgeofdigramfrequencies
22.7Relationtoastochasticmodel
22.8Thenoisychannel

AppendixAOtherapproachestoprobabilitytheory
A.1TheKolmogorovsystemofprobability
A.2ThedeFinettisystemofprobability
A.3Comparativeprobability
A.4Holdoutsagainstuniversalcomparability
A.5Speculationsaboutlatticetheories

AppendixBMathematicalformalitiesandstyle
B.1Notationandlogicalhierarchy
B.2Ourcautiousapproachpolicy
B.3WillyFelleronmeasuretheory
B.4Kroneckervs.Weierstrasz
B.5Whatisalegitimatemathematicalfunction?
B.5.1Delta-functions
B.5.2Nondifferentiablefunctions
B.5.3Bogusnondifferentiablefunctions
B.6Countinginfinitesets?
B.7TheHausdorffsphereparadoxandmathematicaldiseases
B.8WhatamIsupposedtopublish?
B.9Mathematicalcourtesy

AppendixCConvolutionsandcumulants
C.1Relationofcumulantsandmoments
内容简介:
《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。
作者简介:
E.T.Jaynes（1922—1998）已故著名数学家和物理学家。生前曾任华盛顿大学圣路易斯分校和斯坦福大学教授。他因为提出了热动力学的最大熵原理（1957年）和量子光学的Jaynes-Cummings／模型（1963年）而闻名于世。此后的几十年，他一直在探求将概率和统计推断作为整个科学的逻辑基础这一重大课题，其成果和心得最终凝结为本书。
目录:
PartⅠPrinciplesandelementaryapplications
1Plausiblereasoning
1.1Deductiveandplausiblereasoning
1.2Analogieswithslcaltheories
1.3Thethinkingcomputer
1.4Introducingtherobot
1.5Booleanalgebra
1.6Adequatesetsofoperations
1.7Thebasicdesiderata
1.8Comments
1.8.1Commonlanguagevs.formallogic
1.8.2Nitpicking

2Thequantitativerules
2.1Theproductrule
2.2Thesumrule
2.3Qualitativeproperties
2.4Numericalvalues
2.5Notationandfinite-setspolicy
2.6Comments
2.6.1Suectlvevs.oectlve
2.6.2G/3delstheorem
2.6.3Venndiagrams
2.6.4TheKolmogorovaxioms

3Elementarysamplingtheory
3.1Samplingwithoutreplacement
3.2Logicvs.propensity
3.3Reasoningfromlesspreciseinformation
3.4Expectations
3.5Otherformsandextensions
3.6Probabilityasamathematicaltool
3.7Thebinomialdistribution
3.8Samplingwithreplacement
3.8.1Digression：asermononrealityvs.models
3.9Correctionforcorrelations
3.10Simplification
3.11Comments
3.11.1Alookahead

4Elementaryhypothesistesting
4.1Priorprobabilities
4.2Testingbinaryhypotheseswithbinarydata
4.3Nonextensibilitybeyondthebinarycase
4.4Multiplehypothesistesting
4.4.1Digressiononanotherderivation
4.5Continuousprobabilitydistributionfunctions
4.6Testinganinfinitenumberofhypotheses
4.6.1Historicaldigression
4.7Simpleandcompound(orcomposite)hypotheses
4.8Comments
4.8.1Etymology
4.8.2Whathaveweaccomplished?

5Queerusesforprobabilitytheory
5.1Extrasensoryperception
5.2MrsStewartstelepathicpowers
5.2.1Digressiononthenormalapproximation
5.2.2BacktoMrsStewart
5.3Converginganddivergingviews
5.4Visualperception-evolutionintoBayesianity?
5.5ThediscoveryofNeptune
5.5.1Digressiononalternativehypotheses
5.5.2BacktoNewton
5.6Horseracingandweatherforecasting
5.6.1Discussion
5.7Paradoxesofintuition
5.8Bayesianjurisprudence
5.9Comments
5.9.1Whatisqueer?

6Elementaryparameterestimation
6.1Inversionoftheumdistributions
6.2BothNandRunknown
6.3Uniformprior
6.4Predictivedistributions
6.5Truncateduniformpriors
6.6Aconcaveprior
6.7Thebinomialmonkeyprior
6.8Metamorphosisintocontinuousparameterestimation
6.9Estimationwithabinomialsamplingdistribution
6.9.1Digressiononoptionalstopping
6.10Compoundestimationproblems
6.11AsimpleBayesianestimate：quantitativepriorinformation
6.11.1Fromposteriordistributionfunctiontoestimate
6.12Effectsofqualitativepriorinformation
6.13Choiceofaprior
6.14Onwiththecalculation!
6.15TheJeffreysprior
6.16Thepointofitall
6.17Intervalestimation
6.18Calculationofvariance
6.19Generalizationandasymptoticforms
6.20Rectangularsamplingdistribution
6.21Smallsamples
6.22Mathematicaltrickery
6.23Comments

7Thecentral，Gaussianornormaldistribution
7.1Thegravitatingphenomenon
7.2TheHerschel-Maxwellderivation
7.3TheGaussderivation
7.4HistoricalimportanceofGausssresult
7.5TheLandonderivation
7.6WhytheubiquitoususeofGausslandistributions?
7.7Whytheubiquitoussuccess?
7.8Whatestimatorshouldweuse?
7.9Errorcancellation
7.10Thenearirrelevanceofsamplingfrequencydistributions
7.11Theremarkableefficiencyofinformationtransfer
7.12Othersamplingdistributions
7.13Nuisanceparametersassafetydevices
7.14Moregeneralproperties
7.15ConvolutionofGaussians
7.16Thecentrallimittheorem
7.17Accuracyofcomputations
7.18Galtonsdiscovery
7.19PopulationdynamicsandDarwinianevolution
7.20Evolutionofhumming-birdsandflowers
7.21Applicationtoeconomics
7.22ThegreatinequalityofJupiterandSaturn
7.23ResolutionofdistributionsintoGaussians
7.24Hermitepolynomialsolutions
7.25Fouriertransformrelations
7.26Thereishopeafterall
7.27Comments
7.27.1Terminologyagain

8Sufficiency，ancillarity，andallthat
8.1Sufficiency
8.2Fishersufficiency
8.2.1Examples
8.2.2TheBlackwell-Raotheorem
8.3Generalizedsufficiency
8.4Sufficiencyplusnuisanceparameters
8.5Thelikelihoodprinciple
8.6Ancillarity
8.7Generalizedancillaryinformation
8.8Asymptoticlikelihood：Fisherinformation
8.9Combiningevidencefromdifferentsources
8.10Poolingthedata
8.10.1Fine-grainedpropositions
8.11Samsbrokenthermometer
8.12Comments
8.12.1Thefallacyofsamplere-use
8.12.2Afolktheorem
8.12.3Effectofpriorinformation
8.12.4Clevertricksandgamesmanship

9Repetitiveexperiments：probabilityandfrequency
9.1Physicalexperiments
9.2Thepoorlyinformedrobot
9.3Induction
9.4Aretheregeneralinductiverules?
9.5Multiplicityfactors
9.6Partitionfunctionalgorithms
9.6.1Solutionbyinspection
9.7Entropyalgorithms
9.8Anotherwayoflookingatit
9.9Entropymaximization
9.10Probabilityandfrequency
9.11Significancetests
9.11.1Impliedalternatives
9.12Comparisonofpsiandchi-squared
9.13Thechi-squaredtest
9.14Generalization
9.15Halleysmortalitytable
9.16Comments
9.16.1Theirrationalists
9.16.2Superstitions
10Physicsofrandomexperiments
10.1Aninterestingcorrelation
10.2Historicalbackground
10.3Howtocheatatcoinanddietossing
10.3.1Experimentalevidence
10.4Bridgehands
10.5Generalrandomexperiments
10.6Inductionrevisited
10.7Butwhataboutquantumtheory?
10.8Mechanicsundertheclouds
10.9Moreoncoinsandsymmetry
10.10Independenceoftosses
10.11Thearroganceoftheuninformed

PartⅡAdvancedapplications
11Discretepriorprobabilities：theentropyprinciple
11.1Anewkindofpriorinformation
11.2Minimum∑Pi2
11.3Entropy：Shannonstheorem
11.4TheWallisderivation
11.5Anexample
11.6Generalization：amorerigorousproof
11.7Formalpropertiesofmaximumentropydistributions
11.8Conceptualproblems-frequencycorrespondence
11.9Comments

12Ignorancepriorsandtransformationgroups
12.1Whatarewetryingtodo?
12.2Ignorancepriors
12.3Continuousdistributions
12.4Transformationgroups
12.4.1Locationandscaleparameters
12.4.2APoissonrate
12.4.3Unknownprobabilityforsuccess
12.4.4Bertrandsproblem
12.5Comments

13Decisiontheory，historicalbackground
13.1Inferencevs.decision
13.2DanielBernoullissuggestion
13.3Therationaleofinsurance
13.4Entropyandutility
13.5Thehonestweatherman
13.6ReactionstoDanielBernoulliandLaplace
13.7Waldsdecisiontheory
13.8Parameterestimationforminimumloss
13.9Reformulationoftheproblem
13.10Effectofvaryinglossfunctions
13.11Generaldecisiontheory
13.12Comments
13.12.1Objectivityofdecisiontheory
13.12.2Lossfunctionsinhumansociety
13.12.3AnewlookattheJeffreysprior
13.12.4Decisiontheoryisnotfundamental
13.12.5Anotherdimension?

14Simpleapplicationsofdecisiontheory
14.1Definitionsandpreliminaries
14.2Sufficiencyandinformation
14.3Lossfunctionsandcriteriaofoptimumperformance
14.4Adiscreteexample
14.5Howwouldourrobotdoit?
14.6Historicalremarks
14.6.1Theclassicalmatchedfilter
14.7Thewidgetproblem
14.7.1SolutionforStage2
14.7.2SolutionforStage3
14.7.3SolutionforStage4
14.8Comments

15Paradoxesofprobabilitytheory
15.1Howdoparadoxessurviveandgrow?
15.2Summingaseriestheeasyway
15.3Nonconglomerability
15.4Thetumblingtetrahedra
15.5Solutionforafinitenumberoftosses
15.6Finitevs.countableadditivity
15.7TheBorel-Kolmogorovparadox
15.8Themarginalizationparadox
15.8.1Ontogreaterdisasters
15.9Discussion
15.9.1TheDSZExample#5
15.9.2Summary
15.10Ausefulresultafterall?
15.11Howtomass-produceparadoxes
15.12Comments

16Orthodoxmethods：historicalbackground
16.1Theearlyproblems
16.2Sociologyoforthodoxstatistics
16.3RonaldFisher，HaroldJeffreys，andJerzyNeyman
16.4Pre-dataandpost-dataconsiderations
16.5Thesamplingdistributionforanestimator
16.6Pro-causalandanti-causalbias
16.7Whatisreal，theprobabilityorthephenomenon?
16.8Comments
16.8.1Communicationdifficulties

17Principlesandpathologyoforthodoxstatistics
17.1Informationloss
17.2Unbiasedestimators
17.3Pathologyofanunbiasedestimate
17.4Thefundamentalinequalityofthesamplingvariance
17.5Periodicity：theweatherinCentralPark
17.5.1Thefollyofpre-filteringdata
17.6.ABayesiananalysis
17.7Thefollyofrandomization
17.8Fisher：commonsenseatRothamsted
17.8.1TheBayesiansafetydevice
17.9Missingdata
17.10Trendandseasonalityintimeseries
17.10.1Orthodoxmethods
17.10.2TheBayesianmethod
17.10.3ComparisonofBayesianandorthodoxestimates
17.10.4Animprovedorthodoxestimate
17.10.5Theorthodoxcriterionofperformance
17.11Thegeneralcase
17.12Comments

18TheApdistributionandruleofsuccession
18.1Memorystorageforoldrobots
18.2Relevance
18.3Asurprisingconsequence
18.4Outerandinnerrobots
18.5Anapplication
18.6Laplacesruleofsuccession
18.7Jeffreysobjection
18.8Bassorcarp?
18.9Sowheredoesthisleavetherule?
18.10Generalization
18.11Confirmationandweightofevidence
18.11.1Isindifferencebasedonknowledgeorignorance?
18.12Camapsinductivemethods
18.13Probabilityandfrequencyinexchangeablesequences
18.14Predictionoffrequencies
18.15One-dimensionalneutronmultiplication
18.15.1Thefrequentistsolution
18.15.2TheLaplacesolution
18.16ThedeFinettitheorem
18.17Comments

19Physicalmeasurements
19.1Reductionofequationsofcondition
19.2Reformulationasadecisionproblem
19.2.1SermononGaussianerrordistributions
19.3Theunderdeterminedcase：Kissingular
19.4Theoverdeterminedcase：Kcanbemadenonsingular
19.5Numericalevaluationoftheresult
19.6Accuracyoftheestimates
19.7Comments
19.7.1Aparadox

20Modelcomparison
20.1Formulationoftheproblem
20.2Thefairjudgeandthecruelrealist
20.2.1Parametersknowninadvance
20.2.2Parametersunknown
20.3Butwhereistheideaofsimplicity?
20.4Anexample：linearresponsemodels
20.4.1Digression：theoldsermonstillanothertime
20.5Comments
20.5.1Finalcauses

21Outliersandrobustness
21.1Theexperimentersdilemma
21.2Robustness
21.3Thetwo-modelmodel
21.4Exchangeableselection
21.5ThegeneralBayesiansolution
21.6Pureoutliers
21.7Onerecedingdatum

22Introductiontocommunicationtheory
22.1Originsofthetheory
22.2Thenoiselesschannel
22.3Theinformationsource
22.4DoestheEnglishlanguagehavestatisticalproperties?
22.5Optimumencoding：letterfrequenciesknown
22.6Betterencodingfromknowledgeofdigramfrequencies
22.7Relationtoastochasticmodel
22.8Thenoisychannel

AppendixAOtherapproachestoprobabilitytheory
A.1TheKolmogorovsystemofprobability
A.2ThedeFinettisystemofprobability
A.3Comparativeprobability
A.4Holdoutsagainstuniversalcomparability
A.5Speculationsaboutlatticetheories

AppendixBMathematicalformalitiesandstyle
B.1Notationandlogicalhierarchy
B.2Ourcautiousapproachpolicy
B.3WillyFelleronmeasuretheory
B.4Kroneckervs.Weierstrasz
B.5Whatisalegitimatemathematicalfunction?
B.5.1Delta-functions
B.5.2Nondifferentiablefunctions
B.5.3Bogusnondifferentiablefunctions
B.6Countinginfinitesets?
B.7TheHausdorffsphereparadoxandmathematicaldiseases
B.8WhatamIsupposedtopublish?
B.9Mathematicalcourtesy

AppendixCConvolutionsandcumulants
C.1Relationofcumulantsandmoments