Bayesian reasoning in data analysis
A critical introduction

by Giulio D'Agostini

[World Scientific Publishing, 2003]

"Statistics books must take seriously the need to teach the foundations of statistical reasoning from the beginning...
D'Agostini's new book does it admirably, building an edifice od Bayesian statistical reasoning in the physical sciences on solid foundations.

According to the author, the audience for this book is practicing physicists and engineers who need to evaluate uncertainty. To that list, I would like to add upper-level and graduate students in physics and engineering, statisticians and statistics graduate students who collaborate with physicists and engineers, mathematicians who teach statistics courses, and all Bayesian statisticians" (J. Am. Stat. Ass.)


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[ buy from Amazon ] [soft cover (2013) recommended!]

List of contents

Preface

PART 1 - Critical review and outline of the Bayesian alternative

Chapter 1 - Uncertainty in physics and the usual methods of handling it
1.1 Uncertainty in physics [3]
1.2 True value, error and uncertainty [5] 
1.3 Sources of measurement uncertainty [6]
1.4 Usual handling of measurement uncertainties [7]
1.5 Probability of observables versus probability of `true values' [9] 
1.6 Probability of the causes [11]
1.7 Unsuitability of frequentistic confidence intervals [11]
1.8 Misunderstandings caused by the standard paradigm of hypothesis tests [15]
1.9 Statistical significance versus probability of hypotheses  [19]

Chapter 2 - A probabilistic theory of measurement uncertainty
2.1 Where to restart from? [25]
2.2 Concepts of probability  [27]
2.3 Subjective probability [29]
2.4 Learning from observations: the `problem of induction' [32]
2.5 Beyond Popper's falsification scheme [34]
2.6 From the probability of the effects to the probability of the causes [34]
2.7 Bayes' theorem for uncertain quantities [36]
2.8 Afraid of `prejudices'? Logical necessity versus frequent practical irrelevance of priors [37]
2.9 Recovering standard methods and short-cuts to Bayesian reasoning [39]
2.10 Evaluation of measurement uncertainty: general scheme [41]
2.10.1 Direct measurement in the absence of systematic errors [41]
2.10.2 Indirect measurements [42]
2.10.3 Systematic errors [43]
2.10.4 Approximate methods [46]


PART 2 - A Bayesian primer

Chapter 3 - Subjective probability and Bayes' theorem
3.1 What is probability? [51]
3.2 Subjective definition of probability [52]
3.3 Rules of probability [55]
3.4 Subjective probability and `objective' description of the physical world [58]
3.5 Conditional probability and Bayes' theorem [60]
3.5.1 Dependence of the probability on the state of information [60]
3.5.2 Conditional probability [61]
3.5.3 Bayes' theorem [63]
3.5.4 `Conventional' use of Bayes' theorem [66]
3.6 Bayesian statistics: learning by experience [68]
3.7 Hypothesis `test' (discrete case) [71]
3.7.1 Variations over a problem to Newton [72]
3.8 Falsificationism and Bayesian statistics [76]
3.9 Probability versus decision [76]
3.10 Probability of hypotheses versus probability of  observations [77]
3.11 Choice of the initial probabilities (discrete case) [78]
3.11.1 General criteria [78]
3.11.2 Insufficient reason and Maximum Entropy [81]
3.12 Solution to some problems [82]
3.12.1 AIDS test [82]
3.12.2 Gold/silver ring problem [83]
3.12.3 Regular or double-head coin? [84]
3.12.4 Which random generator is responsible for the observed number? [84]
3.13 Some further examples showing the crucial role of background knowledge [85]

Chapter 4 - Probability distributions (a concise reminder)
4.1 Discrete variables [89]
4.2 Continuous variables: probability and probability density function [92]
4.3 Distribution of several random variables [98]
4.4 Propagation of uncertainty [104]
4.5 Central limit theorem [108]
4.5.1 Terms and role [108]
4.5.2 Distribution of a sample average [111]
4.5.3 Normal approximation of the binomial and of the Poisson distribution [111]
4.5.4 Normal distribution of measurement errors [112]
4.5.5 Caution [112]
4.6 Laws of large numbers [113]

Chapter 5 - Bayesian inference of continuous quantities
5.1 Measurement error and measurement uncertainty [115]
5.1.1 General form of Bayesian inference [116]
5.2 Bayesian inference and maximum likelihood [118]
5.3 The dog, the hunter and the biased Bayesian estimators [119]
5.4 Choice of the initial probability density function [120]
5.4.1 Difference with respect to the discrete case [120]
5.4.2 Bertrand paradox and angels' sex [121]

Chapter 6 - Gaussian likelihood
6.1 Normally distributed observables [123]
6.2 Final distribution, prevision and credibility intervals of the true value [124]
6.3 Combination of several measurements -- Role of priors [125]
6.3.1 Update of estimates in terms of Kalman filter [126]
6.4 Conjugate priors [126]
6.5 Improper priors --- never take models literally! [127]
6.6 Predictive distribution [127]
6.7 Measurements close to the edge of the physical region [128]
6.8 Uncertainty of the instrument scale offset [131]
6.9 Correction for known systematic errors [133]
6.10 Measuring two quantities with the same instrument having an uncertainty of the scale offset [133]
6.11 Indirect calibration [136]
6.12 The Gauss derivation of the Gaussian [137]

Chapter 7 - Counting experiments
7.1 Binomially distributed observables [141]
7.1.1 Observing 0\% or 100\% [145]
7.1.2 Combination of independent measurements [146]
7.1.3 Conjugate prior and many data limit [146]
7.2 The Bayes problem [148]
7.3 Predicting relative frequencies -- Terms and interpretation of Bernoulli's theorem [148]
7.4 Poisson distributed observables [152]
7.4.1 Observation of zero counts [154]
7.5 Conjugate prior of the Poisson likelihood [155]
7.6 Predicting future counts [155]
7.7 A deeper look to the Poissonian case [156]
7.7.1 Dependence on priors --- practical examples [156]
7.7.2 Combination of results from similar experiments [158]
7.7.3 Combination of results: general case [160]
7.7.4 Including systematic effects [162]
7.7.5 Counting measurements in the presence of background [165]

Chapter 8 - Bypassing Bayes' theorem for routine applications
8.1 Maximum likelihood and least squares as particular cases of Bayesian inference [169]
8.2 Linear fit [172]
8.3 Linear fit with errors on both axes [175]
8.4 More complex cases [176]
8.5 Systematic errors and `integrated likelihood' [177]
8.6 Linearization of the effects of influence quantities and approximate formulae [178]
8.7 BIPM and ISO recommendations [181]
8.8 Evaluation of type B uncertainties [183]
8.9 Examples of type B uncertainties [184]
8.10 Comments on the use of type B uncertainties [186]
8.11 Caveat concerning the blind use of approximate methods [189]
8.12 Propagation of uncertainty [191]
8.13 Covariance matrix of experimental results -- more details [192]
8.13.1 Building the covariance matrix of experimental data [192]
8.13.1.1 Offset uncertainty [193]
8.13.1.2 Normalization uncertainty [195]
8.13.1.3 General case [196]
8.14 Use and misuse of the covariance matrix to fit correlated data [197]
8.14.1 Best estimate of the true value from two correlated values [197]
8.14.2 Offset uncertainty [198]
8.14.3 Normalization uncertainty [198]
8.14.4 Peelle's Pertinent Puzzle [202]

Chapter 9 - Bayesian unfolding
9.1 Problem and typical solutions [203]
9.2 Bayes' theorem stated in terms of causes and effects [204]
9.3 Unfolding an experimental distribution [205]


PART 3 - Further comments, examples and applications

Chapter 10 - Miscellanea on general issues in probability and inference
10.1 Unifying role of subjective approach [211]
10.2 Frequentists and combinatorial evaluation of probability [213]
10.3 Interpretation of conditional probability [215]
10.4 Are the beliefs in contradiction to the perceived  objectivity of physics? [216]
10.5 Frequentists and Bayesian `sects' [220]
10.5.1 Bayesian versus frequentistic methods [221]
10.5.2 Subjective or objective Bayesian theory? [222]
10.5.3 Bayes' theorem is not everything [226]
10.6 Biased Bayesian estimators and Monte Carlo checks of Bayesian procedures [226]
10.7 Frequentistic coverage [229]
10.7.1 Orthodox teacher versus sharp student - a dialogue by George Gabor [232]
10.8 Why do frequentistic hypothesis tests `often work'? [233]
10.9 Comparing `complex' hypotheses -- automatic Ockham' Razor [239]
10.10 Bayesian networks [241]
10.10.1 Networks of beliefs -- conceptual and practical applications [241]
10.10.2 The gold/silver ring problem in terms of Bayesian networks [242]

Chapter 11 - Combination of experimental results: a closer look
11.1 Use and misuse of the standard combination rule [247]
11.2 `Apparently incompatible' experimental results [249]
11.3 Sceptical combination of experimental results [252]
11.3.1 Application to epsilon'/epsilon [259]
11.3.2 Posterior evaluation of sigma_i [262]

Chapter 12 - Asymmetric uncertainties and nonlinear propagation
12.1 Usual combination of `statistic and systematic errors' [267]
12.2 Sources of asymmetric uncertainties in standard statistical procedures [269]
12.2.1 Asymmetric chi2 and ``Delta_chi2 =1 rule'[269]
12.2.2 Systematic effects [272]
12.2.2.1 Asymmetric beliefs on systematic  effects [273]
12.2.2.2 Nonlinear propagation of uncertainties [273]
12.3 General solution of the problem [273]
12.4 Approximate solution [275]
12.4.1 Linear expansion around E[X] [276]
12.4.2 Small deviations from linearity [278]
12.5 Numerical examples [280]
12.6 The non-monotonic case [282]

Chapter 13 Which priors for frontier physics?
13.1 Frontier physics measurements at the limit to the detector sensitivity [285]
13.2 Desiderata for an optimal report of search results [286]
13.3 Master example: Inferring the intensity of a Poisson  process in the presence of background [287]
13.4 Modelling the inferential process [288]
13.5 Choice of priors [288]
13.5.1 Uniform prior [289]
13.5.2 Jeffreys' prior [290]
13.5.3 Role of priors [292]
13.5.4 Priors reflecting the positive attitude of researchers [292]
13.6 Prior-free presentation of the experimental evidence [295]
13.7 Some examples of R-function based on real data [298]
13.8 Sensitivity bound versus probabilistic bound [299]
13.9 Open versus closed likelihood [302]


PART 4 -  Conclusion

Chapter  14 - Conclusions and bibliography
14.1 About subjective probability and Bayesian inference] 307}
14.2 Conservative or realistic uncertainty evaluation? [308]
14.3 Assessment of uncertainty is not a mathematical game [310]
14.4 Bibliographic note [310]


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See e.g. Y.L. Dokshitzer, ``DIS 96/97. Theory/Developments'', Proc. 5th International Workshop on Deep Inelastic Scattering and QCD, Chicago, April 1997, J. Repond and D. Krakauer eds. (AIP Conf. Proc. 407) [hep-ph/9706375]. [ buy from Amazon ]

101
See e.g. G. Altarelli, ``The status of the Standard Model'', talk at 18th International Symposium on Lepton-Photon Interactions, Hamburg, August 1997, CERN-TH-97-278, Oct. 1997 [hep-ph/9710434].

102
R. Feynman, ``The character of the physical law'', The MIT Press, 1967 [ buy from Amazon ]

103
B. Efron, ``Why isn't everyone a Bayesian?'', Am. Stat. 40 (1986) 1, with discussion on pages 6-11.

104
D.V. Lindley, comment to Ref. [103], Am. Stat. 40 (1986) 6.

105
A. Zellner, ``Bayesian solution to a problem posed by Efron'', Am. Stat. 40 (1986) 330.

106
B. Efron, reply to Ref. [105], Am. Stat. 40 (1986) 331.

107
J.M. Bernardo, ``Non-informative priors do not exist'', J. Stat. Plan. and Inf. 65 (1997) 159, including discussions by D.R. Cox, A.P. Dawid, J.K. Ghosh and D. Lindley, pp. 177-189.

108
E.T. Jaynes, ``Probability theory: the logic of science'', book in preparation, see http://omega.albany.edu:8008/JaynesBook.html. (recently while this book was in print [ buy from Amazon ])

109
G. Zech, ``Objections to the unified approach to the computation of classical confidence limits'', physics/9809035 (see Ref. [11] for more extensive argumentations).

110
R.D. Cousins, ``Why isn't every physicist a Bayesian?'', Am. J. Phys. 63 (1995) 398.

111
G. Feldman, Panel Discussion at Workshop on Confidence Limits, Geneva, Switzerland, January 2000, CERN Report 2000-005, p. 277. [http://ep-div.web.cern.ch/ep-div/Events/CLW/papers.html].

112
G. Gabor (gabor@is.dal.ca), private communication, 1999.

113
A. de Rujula, ``Snapshots of the 1985 high energy physics panorama'', Proc. of the International Europhysics Conference on High-Energy Physics, Bari (Italy), July 1995, L. Nitti and G. Preparata eds.

114
G. Salvini, Welcome address to the International Workshop on Deep Inelastic Scattering and related phenomena, Roma (Italy), April 1996; World Scientific, 1997, G. D'Agostini and A. Nigro eds. [ buy from Amazon ]

115
J.O. Berger and W.H. Jefferys, ``Sharpening Ockham's razor on a Bayesian strop'', Am. Scientist 89 (1992) 64 and Journal of the Italian Statistical Society 1 (1992) 17
[http://quasar.as.utexas.edu/Papers.html].

116
T.J. Loredo and D.Q. Lamb, Bayesian analysis of neutrinos observed from supernova SN 1987A, Phys. Rev. D65 (2002) 063002 [astro-ph/0107260>].

117
M.V. John and J.V. Narlikar, ``Comparison of cosmological models using Bayesian theory'', Phys.Rev. D65 (2002) 043506 [astro-ph/0111122].

118
M.P. Hobson, S.L. Bridle and O. Lahav, ``Combining cosmological datasets: hyperparameters and Bayesian evidence'', 2002, astro-ph/0203259.

119
C.E. Rasmussen and Z. Ghahramani, ``Occam's Razor'', Neural Information Processing Systems 13 (2001) [http://www.gatsby.ucl.ac.uk/~zoubin/papers.html], see also http://www.gatsby.ucl.ac.uk/~zoubin/talks/cmu-talk.pdf.

120
See, e.g, J. Pearl, ``Probabilistic reasoning in intelligent systems: networks of plausible inference'', Morgan Kaufmann Publishers, 1988. [ buy from Amazon ]
F.V. Jensen, ``An introduction to Bayesian networks'', UCL Press (and Springer Verlag), 1996. [ buy from Amazon ]
D. Heckerman and M.P. Wellman, ``Bayesian Networks'', Communications of the ACM (Association for Computing Machinery), Vol. 38, No. 3, March 1995, p. 27.
L. Burnell and E. Horvitz, ``Structure and chance: melding logic and probability for software debugging'', ibid., p. 31.
R. Fung and B. Del Favero, ``Applying Bayesian networks to Information retrieval'', ibid., p. 42.
D. Heckerman, J.S. Breese and K. Rommelse, ``Decision-theoretic troubleshooting'', ibid., p. 49.
R.G. Cowell, A.P. Dawid, S.L. Lauritzen and D.J. Spiegelhalter ``Probabilistic Networks and Expert Systems'', Springer Verlag, 1999. [ buy from Amazon ]
http://www.auai.org/
http://bayes.stat.washington.edu/almond/belief.html.

121
J.B. Kadane and D.A. Schum, ``A Probabilistic analysis of the Sacco and Vanzetti evidence'', J. Wiley and Sons, 1996. [ buy from Amazon ]
P. Garbolino and F. Taroni, ``Evaluation of scientific evidence using Bayesian networks'', Forensic Science International 125 (2002) 149, and references therein.

122
F.B Cozman, ``JavaBayes version 0.346 - Bayesian networks in Java'', January 2001, http://www-2.cs.cmu.edu/~javabayes/Home/

123
http://www.roma1.infn.it/~dagos/bn/

124
D.J. Spiegelhalter, A. Thomas and N.G. Best (et al.), ``Bayesian inference Using Gibbs Sampling'',
W.R. Gilks, S. Richardson and D.J. Spiegelhalter, ``Markov Chain Monte Carlo Methods in Practice'', Chapman and Hall, 1996.
http://www.mrc-bsu.cam.ac.uk/bugs/welcome.shtml.

125
http://www.statslab.cam.ac.uk/~mcmc/

126
NA 48 Collaboration, J.R. Batley and al., ``A precise measurement of direct CP violation in the decay of neutral kaons into two pions'', Phys.Lett B544 (2002) 97 [hep-ex/0208009].

127
G. D'Agostini, ``Sceptical combination of experimental results: General considerations and application to epsilon'/epsilon'', CERN-EP/99-139, October 1999, hep-ex/9910036, and references therein.

128
M. Fabbrichesi, ``Estimating epsilon'/epsilon. A user's manual'', Nucl. Phys. Proc. Suppl. 86 (2000) 322 [hep-ph/9909224].

129
V. Dose and W. von der Linden, ``Outlier tolerant parameter estimation'', Proc. of the XVIII International Workshop on Maximum Entropy and Bayesian Methods, Garching (Germany), July 1998, V. Dose et al. eds., Kluwer Academic Publishers, Dordrecht, 1999 [http://www.ipp.mpg.de/OP/Datenanalyse/Publications/].

130
W.H. Press, ``Understanding data better with Bayesian and global statistical methods'', Conference on Some Unsolved Problems in Astrophysics, Princeton, NJ, 27-29 Apr 1995 [astro-ph/9604126].

131
C. Pascaud and F. Zomer, ``QCD analysis from the proton structure function measurement: issues on fitting, statistical and systematic errors'', LAL 95-05, June 1995 [http://www-h1.desy.de/h1work/fit/ h1fit.info.html].

132
S. Alekhin, ``Extraction of parton distributions and alphas from DIS data within the Bayesian treatment of systematic errors'', Eur. Phys. J. C10 (1999) 395 [hep-ph/9611213].

133
M. Botje, ``A QCD analysis of HERA and fixed target structure function data'', ZEUS Note 98-062 DESY-99-038, December 1999 [hep-ph/9912439].

134
R.S. Thorne et al. ``Questions on uncertainties in parton distributions'', Conference on Advanced Statistical Techniques in Particle Physics, March 2002, Durham, hep-ph/0205233.

135
H. Wahl (CERN), private communication, 1999.

136
G. D'Agostini and M. Raso, ``Uncertainties due to imperfect knowledge of systematic effects: general considerations and approximate formulae'', CERN-EP/2000-026, February 2000 [hep-ex/0002056].

137
P. Astone and G. D'Agostini, ``Inferring the intensity of Poisson processes at the limit of the detector sensitivity (with a case study on gravitational wave burst search)'', CERN-EP/99-126, August 1999 [hep-ex/9909047].

138
P. Astone at al., ``Search for correlation between GRB's detected by BeppoSAX and gravitational wave detectors EXPLORER and NAUTILUS'', Phys. Rev. 66 (2002) 102002 [astro-ph/0206431].

139
T.J. Loredo, ``The promise of Bayesian inference for astrophysics'', Proc. Statistical Challenges in Modern Astronomy, E.D. Feigelson and G.J. Babu eds., Springer-Verlag (1992) 275 [http://astrosun.tn.cornell.edu/staff/loredo/bayes/tjl.html]. This web site contains also other interesting tutorials, papers and links on Bayesian analysis.

140
ZEUS Collaboration, ``Search for contact interactions in deep inelastic e++p->e++X scattering at HERA'', Eur. Phys. J C14 (2000) 239 [hep-ex/9905039].

141
CELLO Collaboration, H.J. Behrend et al., ``Search for substructures of leptons and quark with CELLO detector'', Z. Phys. C51 (1991) 149.

142
G. D'Agostini and G. Degrassi, ``Constraining the Higgs boson mass through the combination of direct search and precision measurement results'', Contribution to the Workshop on ``Confidence Limits'', CERN, Geneva, 17-18 January 2000 [hep-ph/0001269].

143
R. Feynman, 1973 Hawaii Summer Institute, cited by D. Perkins at the 1995 EPS Conference, Brussels.

144
C. Howson and P. Urbach, ``Scientific reasoning - the Bayesian approach'', Open Court, 1993 (second edition). [ buy from Amazon ]

145
J. Earman, ``Bayes or bust? A critical examination of Bayesian confirmation theory'', The MIT Press, 1992. [ buy from Amazon ]

146
R. Jeffrey, ``Probabilistic thinking'', 1995, http://www.princeton.edu/bayesway/ProbThink/

147
M. Kaplan, ``Decision theory as philosophy'', Cambridge University Press, 1996. [ buy from Amazon ]

148
R. Jeffrey, ``Subjective Probability (The Real Thing)'', 2002 http://www. princeton.edu/bayesway/Book*.pdf. Related essays can be found at 'http://www.princeton.edu/bayesway/.

149
J.M. Bernardo, ``Bayesian statistics'', UNESCO Encyclopedia of Life Support Systems (EOLSS) [ftp://matheron.uv.es/pub/personal/bernardo/BayesStat.pdf].

150
F. Spizzichino, ``Subjective probability models for lifetimes'', Boca Raton Chapman & Hall/CRC, 2001. [ buy from Amazon ]

151
B. de Finetti, ``Filosofia della probabilità'', il Saggiatore, 1995. [ buy from Amazon ]

152
L. Piccinato, ``Metodi per le decisioni statistiche'', Springer-Italia, 1996.

153
D. Costantini e P. Monari (eds.), ``Probabilità e giochi d'azzardo'', Franco Muzzio Editore, 1996.

154
R. L. Winkler, ``An introduction to Bayesian inference and decision'', Holt, Rinehart and Winston, Inc., 1972. [ buy from Amazon ]

155
S. J. Press, ``Bayesian statistics: principles, models, and applications'', John Wiley & Sons, 1989. [ buy from Amazon ]

156
G.E.P. Box and G.C. Tiao, ``Bayesian inference in statistical analysis'', John Wiley and Sons, 1973. [ buy from Amazon ]

157
A. O'Hagan, ``Probability: methods and measurements'', Chapman & Hall, 1988. [ buy from Amazon ]

158
P.M. Lee, ``Bayesian statistics - an introduction'', John Wiley and Sons, 1997. [ buy from Amazon ]

159
L.J. Savage et al., ``The foundations of statistical inference: a discussion'', Methuen, 1962. [ buy from Amazon ]

160
A. Zellner, ``Bayesian analysis in econometrics and statistics'', Eduard Elgar, 1997. [ buy from Amazon ]

161
J.M. Bernardo et al., Valencia Meetings on ``Bayesian Statistics'' 1-7, http://www.uv.es/bernardo/valenciam.html. Latest issues: 7 [ buy from Amazon ]; 6 [ buy from Amazon ]; 5 [ buy from Amazon ]

162
G.L. Bretthorst ``Bayesian spectrum analysis and parameter estimation'', Springer Verlag, 1988 [http://bayes.wustl.edu/glb/book.pdf].

163
A. Pole, M. West and P.J. Harrison ``Applied Bayesian Forecasting and Time Series Analysis'', 1994, Chapman-Hall. [ buy from Amazon ] More information and related software can be found at http://www.isds.duke.edu/~mw/books_software_data.html.

164
'http://www.bayesian.org/
http://www.amstat.org/sections/SBSS/
http://bayes.stat.washington.edu/bayes_people.html
http://www.ar-tiste.com/blip.html
http://www.strauss.lanl.gov/Welcome.html
http://fourier.dur.ac.uk:8000/stats/bayeslin/
http://astrosun.tn.cornell.edu/staff/loredo/bayes/.

165
http://astrosun.tn.cornell.edu/staff/loredo/bayes/tjl.html

166
http://www.ipp.mpg.de/OP/Datenanalyse/ http://public.lanl.gov/kmh/publications/publications.html

167
Uncertainty Quantification Working Group, http://public.lanl.gov/ kmh/uncertainty/

168
A.F.M. Smith, ``Bayesian numerical analysis'', Phil. Trans. R. Soc. London 337 (1991) 369.

169
R.M. Neal, ``Probabilistic inference using Markov Chain Monte Carlo Methods'', Technical Report CRG-TR-93-1, University of Toronto, 1993, ftp://ftp.cs.utoront.ca/pub/radford/review.pdf.

170
W.R. Gilks, S. Richardson and D.J. Spiegelhalter ``Markov Chain Monte Carlo in practice'', Chapman and Hall, 1996. [ buy from Amazon ]

171
R.E. Kass, B.P. Carlin, A. Gelman and R.M. Neal, ``Markov Chain Monte Carlo in practice: A roundtable discussion'', Am. Stat. 52 (1998) 93 [http://www.amstat.org/publications/tas/kass.pdf].

172
K.M. Hanson, ``Tutorial on Markov Chain Monte Carlo'', XX International Workshop on Maximum Entropy and Bayesian Methods in Science and Engineering, Gif-sur-Yvette (France), July 2000, [ buy from Amazon ]

173
A. Lewis and S. Bridle, ``Cosmological parameters from CMB and other data: a Monte-Carlo approach'', Phys. Rev. D66 (2002) 103511 [astro-ph/0205436].

174
http://cerebro.xu.edu/math/Sources/.


| Top | CONTENTS | hypertexted BIBLIOGRAPHY | INDEX | ERRATA | Book reviews | Author Home Page |

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Index

     "Delta chi^2 = 1" rule, 170, 269--271
     "Delta ln L =1/2" rule, 269
     3 sigma rule, 236
    
     AIDS test problem
       formulation, 20
       solution, 82
     Anderson C.D., 218
     approximate methods, 39, 41, 46
     arbitrariness and subjectivism, 30
     Aristoteles, 229
     Astone P., 166
     asymmetric uncertainty, 267
     average, 32, 90, 93
       distribution, 111
       probability, 9
     axioms of probability, 29
    
     background in counting experiments, 165
     Basu S., 233
     Bayes factor, 72, 82, 239, 296
     Bayes T., 52
     Bayes' theorem, 32, 36, 63--65, 99
       criticism of `conventional use', 67
     Bayesian, 32
       estimators, 226
       inference, 34, 116
       networks, 241, 242, 244, 246
       statistics, 68
     belief
       degree of, 29, 32, 53
       networks, 241, 242, 244, 246
     Bernardo J.M., 223
     Bernoulli J., 52
     Bernoulli's theorem, 113, 148--150
     Berry D.A., 218, 232
     Bertrand paradox, 121, 122
     bet
       and probability, 29
       coherent, 54
       coherent bet, 29
       odds, 54
     beta distribution, 97
     betting odds, 55
     binomial
       distribution, 91
       likelihood, 41, 141
     BIPM, 181
       recommendation INC-1, 31
     black hole, 218
     blending factor, 126
     bound
       probabilistic, 299, 301
       sensitivity, 299, 301
     branching ratio, 141
    
     CELLO, 199
     central limit theorem, 110--113, 183, 187
       terms, 108
     chi-square
       $Delta \chi^2 = 1$ rule, 170, 269--271
       distribution, 96
       minimization (fit), 170, 269--271
       test, 236
     coherence, 29, 55, 213, 216, 226
     coherent bet, 54
     Coletti G., 225
     combination of results
       binomial model, 146
       Gaussian model, 125, 247
       outliers, 247
       Poisson model, 158--162
       sceptical combination, 252--254
     combinatorial `definition' of probability, 30
     complete class, 58
     conditional inference, 44
     conditional probability, 60--62, 215, 216
     conditioning, 32
     confidence (probability), 73
     confidence interval (frequentistic), 11, 232
     conjugate prior, 126
       binomial likelihood, 146
       Gaussian likelihood, 126
       Poisson likelihood, 155
     contradiction
       proof by, 15
     correlation
       between events, 63
       coefficient, 99
       due to common systematics, 192
       due to systematics, 133, 134, 179--181, 193, 195
     correlation matrix, 101
     counting experiments, 141
     covariance, 99
       matrix
           misuse in fits, 197
           of experimental results, 192, 193, 195
     covariance matrix, 101
     coverage, 229--231, 301
     Cox R.T., 57
     credibility interval, 124
     cumulative function, 90, 93
     Cygnus X-1, 218
    
     de Finetti B., 3, 26, 27, 51, 55, 60, 88, 142, 150, 225
       representation theorem, 28
     de Rujula A., 238
     decision theory, 76
     deduction, 34
     degree of belief, 29, 32, 53
     Descartes' cogito, 26
     deterministic law, 5
     DIN, 115
     dog-hunter, 12, 119
     Dose V., 253
    
     edge of physical region
       measurement at the, 12, 128
     efficiencies, 42
     Efron B., 221
     Einstein A., 25, 26, 30
     empirical law of chance, 150
     entropy, 82
     equiprobability, 52
     error, 4, 5, 115, 116
       normal distributed, 41
       statistical, 8
       systematic, 8, 43
     events, 53
     evidence, 239, 240
     exchangeability, 28, 142
     expected gain, 76
     expected value, 90, 93, 99
     exponential distribution, 95
    
     falsification scheme, 34
     falsificationism, 76
     Fermi E., 171
     Feynman R., 51, 220
     final probability, 65
     finite partition, 58
     Fisher R.A., 172
     fit, 172--174
     Franklin A., 217
     fuzzy logic, 26
    
     Gabor G.
       a Socratic exchange, 232, 233
     Galilei G., 211
     Galison P., 218
     gamma distribution, 95
     Gauss K.F., 52, 137--139, 172
     Gaussian
       distribution, 94
       distribution of error, 112
       Gauss derivation, 137--139
       likelihood, 41, 123
     gold/silver ring problem
       Bayesian network solution, 242, 244, 246
       formulation, 67
       solution, 83
     good sense, 52
     gravitational constant, 59
    
     Hawking S., 218
     HERA `events', 21, 220
     hidden variables, 30
     Higgs boson, 78
       claim of discovery, 23
     Howson C., 11
     Hume D., 25, 26, 28, 33
     hunter-dog, 12, 119
     hypotheses
       probability of, 19
     hypothesis
       test (frequentistic), 15, 233
    
     implication, 58
     improper priors, 127
     independence, 63
     indifference principle, 81
     indirect measurements, 42
     induction, 32, 34
     influence quantity, 43, 116, 117
     information entropy, 82
     initial probability, 65
     innovation, 126
     input quantity, 273
     intersubjectivity, 31
     ISO, 5, 115, 181
       Guide, 5, 31, 53, 308, 310
    
     Jacobian, 105
     JavaBayes, 242, 243
     Jaynes E., 57
       Jaynes' robot, 223
     Jeffreys H., 57, 221
       priors, 223, 290--293
    
     Kalman filter, 126
     Kant I., 25, 26
     kurtosis, 185, 279
    
     Lad F., 225
     Laplace P.-S., 30, 51, 52, 141, 225
       recursive formula, 144
       rule of succession, 144
     laws of large numbers, 113
     learning by experience, 68
     least squares, 39, 40, 170
     likelihood, 35, 36
       $Delta \chi^2 = 1$ rule, 269
       binomial, 41
       closed, 285, 302
       Gaussian, 41, 123
       maximumemph  {see} mximum likelihood, 170
       open, 285, 302
       Poisson, 41
       principle, 170, 229, 236
     Linden W. von der, 253
     linear fit, 172--174
     linearization, 178
     logical product, 58
     logical sum, 58
     lower limit
       binomial model, 145
    
     Mach E., 26
     marginalization, 98
     maximum bounds, 8
     Maximum Entropy, 57, 82
     maximum entropy, 223
     maximum likelihood, 39, 40, 118, 122, 169, 170
     mean, 90, 93
     measurand, 6
     Millikan R., 252
     mode, 32
     moments, 91
       central, 91
     Moore D., 222
     multinomial distribution, 40, 103
    
     negative mass, 12, 128
     Newton I., 72
     non-informative priors, 223
     normal, see {Gaussian}{94}
     null hypothesis, 15
     null observation, 154
    
     objective Bayesian theory, 222
     objective inference, 223
     objectivity of physics, 216--218
     Ockham' Razor, 239, 240
     odds in betting, 54
     operational subjectivism, 225
     Orear J., 171
     outliers, 247
     output quantity, 273
    
     p-value, 16
     Particle Data Group (PDG), 213, 221, 248, 259, 260, 268, 269
     particle identification, 66
     Pauli W., 51
     Pearson chi-square, 40, 96, 103
     Peelle's Pertinent Puzzle, 202
     penalization, 55
     Pizzella G., 166
     Poincar'e H., 11, 25, 30, 38, 115, 238
     Poisson
       distribution, 92
       likelihood, 41, 152
       process, 95, 287
     Polya G., 213
     Popper K.R., 34, 76
     positive attitude (of researchers), 131, 293
     posterior, 65
     predictive distribution
       binomial likelihood, 151
       Gaussian likelihood, 127
       Poisson likelihood, 155
     prevision, 17, 124
     prior knowledge, 33
     priors, 36--38, 40, 65, 120, 125, 126
       conjugate, 126
       logical necessity, 37, 238
       motivated by `positive attitude', 131
       non-informative, 223
       objective, 223
     probabilistic law, 4
     probability
       ``does not exists'', 60
       axioms, 29, 55
       basic rules, 29, 55
       classical, 52
       classical view, 27
       combinatorial definition, 51
       concepts, 27
       conditional, 60--62
       density function, 32, 92
       distribution
           beta, 97
           binomial, 91
           bivariate Gaussian, 101
           chi-square, 96
           conditional, 98
           Erlang, 96
           exponential, 95
           gamma, 95
           Gaussian, 94, 185, 187
           marginal, 98
           multinomial, 40, 103
           normal, see {Gaussian}{94}
           Poisson, 92
           triangular, 97, 185, 187
           triangular asymmetric, 185, 187
           uniform, 94, 185, 187
       favorable over possible cases, 51
       frequentistic definition, 51
       frequentistic view, 27
       function, 32, 90
       inversion, 10, 14
       Laplace `definition', 30, 52
       logical view, 27
       objective, 28
       of causes, 11, 34
       of hypotheses, 19, 77
       of observations, 77
       standard `definitions', 30
       statistical view, 27
       subjective, 28, 29, 52, 58
     proof by contradiction, 15
     propagation of uncertainties, 8, 42, 44, 104--108, 191
       linearization, 178--181, 276--278
       non-monotonic case, 282
       nonlinear, 273, 278, 279
     proportions, 42
    
     quantum mechanics, 29
    
     random variables, 31, 89
     relative belief updating ratio, 296
     repeatability, 7
     reproductive property, 111
    
     Salvini G., 237
     Schrödinger E., 53, 57, 60, 142, 225
     Scozzafava R., 225
     sensitivity
       analysis, 71, 188, 303
       bound, 299, 301
       coefficient, 108
     sets
       properties, 56
       versus events, 58
     shape distortion function, 296
     signal to noise ratio, 66
     significance
       level, 15
       probabilities, 16
       statistical, 19
     skewness, 185, 279
     smearing, 204
     Smith A.F.M., 221, 223
     standard deviation, 32, 91
     standard statistical methods
       recovering, 39
     statistical effects, 7
     statistical error, 8
     statistical significance, 19
     supersymmetric particles, 59
     systematic effects, 7
     systematic error, 8, 43
       correlation, 133, 134
       linearization, 178--181
       normalization, 195
       of known size, 133
       offset, 131, 193
       Poisson model, 162
    
     tail, probability of, 22
     Thorne K., 218
     top quark, 59
     Tribus M., 82
     true value, 5--7
       probability of, 9
     type A uncertainty, 133, 181
     type B uncertainty, 133, 181--184, 186
    
     uncertain numbers, 31, 89
     uncertainty, 4, 5, 115, 116
       `standard' treatment, 7
       asymmetric, 267
       propagation, 8, 42, 44, 104--108, 191, 268
       source, 3
       sources (ISO), 6
     uncertainty and probability, 29
     unfolding, 203--206, 208
     uniform distribution, 94
     upper limit
       binomial model, 145
       Poisson model, 154, 157--164, 166
     Urbach P., 11
    
     variance, 32, 90, 99
     Venn diagrams, 56
     von Mises R., 67, 213
    
     Weise K., 182
     Wittgenstein L., 13
    
     Zech G., 229
     Zellner A., 221
     Zeno's paradox, 92

Errata

(These corrections have been applied to the second reprint, released in summer 2005)
Other typos (also in second reprint):

Book reviews

| Top | CONTENTS | hypertexted BIBLIOGRAPHY | INDEX | ERRATA | Book reviews | Author Home Page |

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