Bayesian reasoning in data analysis
A critical introduction
by Giulio D'Agostini
"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 upperlevel 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.)
 Top  CONTENTS 
hypertexted BIBLIOGRAPHY 
INDEX 
ERRATA  Book reviews 
Author Home Page 
[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 shortcuts 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 doublehead 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 nonmonotonic 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 Priorfree presentation of the experimental evidence [295]
13.7 Some examples of Rfunction 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]
 Top  CONTENTS 
hypertexted BIBLIOGRAPHY 
INDEX 
ERRATA  Book reviews 
Author Home Page 
Bibliography

 1

G. D'Agostini, ``Probability and measurement uncertainty
in Physics  a Bayesian primer'', Internal Report N. 1070
of the Dept. of Physics
of the Rome University ``La Sapienza'', and DESY95242, December 1995.
[hepph/9512295].
 2

G. D'Agostini, ``Bayesian reasoning in High Energy Physics 
principles and applications'',
CERN Report 9903, July 1999.
[http://www.roma1.infn.it/dagos/YR.html]
 3
 Deutsches Institut für Normung (DIN),
``Grunbegriffe der Messtechnick  Behandlung
von Unsicherheiten bei der Auswertung von Messungen''
(DIN 1319 Teile 14),
Beuth Verlag GmbH, Berlin, Germany, 1985.
Only parts 13
are published in English. An English translation
of part 4 can be requested from the authors of Ref. [36].
Part 3 is going to be rewritten in order to be made in agreement
with Ref. [5] (private communication from K. Weise).
 4
 R. Kaarls, BIPM proc.Verb. Com. Int.
Poids et Mesures 49 (1981), A1A2 (in French);
P. Giacomo, Metrologia 17 (1981) 73 (draft of
English version; for the official BIPM translation see Refs. [5] or [7]).
 5
 International Organization for Standardization (ISO),
``Guide to the expression of uncertainty in measurement'',
Geneva, Switzerland, 1993.
 6
 International Organization for Standardization (ISO),
``International vocabulary of basic and general terms in
metrology'',
Geneva, Switzerland, 1993.
 7
 B.N. Taylor and C.E. Kuyatt,
``Guidelines for evaluating and expressing
uncertainty of NIST measurement results'', NIST Technical Note 1297,
September 1994
[http://physics.nist.gov/Pubs/guidelines/outline.html].
 8
 H. Poincaré, ``Science and Hypothesis'', 1905
(Dover Publications, 1952).
 9
 H. Poincaré, ``Calcul des probabilités'', University of Paris, 189394.
 10
 C. Howson and P. Urbach, ``Bayesian reasoning in science'',
Nature, Vol. 350, 4 April 1991, p. 371.
 11

G. Zech, ``Frequentist and Bayesian confidence limits'',
EPJdirect C12 (2002) 1
[hepex/0106023]
 12

P. Clifford, ``Interval estimation as viewed from the world
of mathematical statistics'',
Workshop on Confidence Limits, Geneva, Switzerland,
January 2000, CERN Report 2000005
[http://epdiv.web.cern.ch/epdiv/Events/CLW/papers.html].
 13
 J.O. Berger and D.A. Berry, ``Statistical analysis and the
illusion of objectivity'', Am. Scientist 76 (1988) 159.
 14
 M.J. Schervish,
``P values: what they are and what they
are not'', Am. Stat. 50 (1996) 203.
 15
 G. Cowan, ``Statistical data analysis'', Clarendon Press, Oxford, 1998.
 16
 B. de Finetti, ``Theory of probability'',
J. Wiley & Sons, 1974.
 17
 K. Baklawsky, M. Cerasoli and G.C. Rota,
``Introduzione alla Probabilità'',
Unione Matematica Italiana, 1984.
 18
 www.desy.de/prinfo/desyrecentheraresultsfeb97_e.html,
(``DESY Science Information on Recent HERA Results'',
Feb. 19, 1997).
 19

DESY'98  Highlights from the DESY Research Center,
``Throwing `heads' seven times in a row 
what if it was just a statistical
fluctuation?''.
 20
 ZEUS Collaboration, J. Breitweg et al., ``Comparison of
ZEUS data with Standard Model predictions for e+p > e+X
scattering at high x Q^2'',
Z. Phys. C74 (1997) 207
[hepex/9702015];
H1 Collaboration, C. Adloff et al.,
``Observation of events at very high Q^2 in
collisions at HERA'', Z. Phys. C74 (1997) 191
[hepex/9702012];
 21

C. Tully in an interview to Physics Web, September 2000:
``Higgs boson on the horizon'',
by V. Jamieson,
http://PhysicsWeb.org/article/news/4/9/2/1.
 22

G. Bunce, in BNL News Release ``Physicists announce possible violation
of standard model of particle physics'', February 2001,
http://www.bnl.gov/bnlweb/pubaf/pr/bnlpr020801.htm.
 23

FNAL, Press Pass November 7, 2001,
``Neutrino Measurement Surprises Fermilab Physicists'',
http://www.fnal.gov/pub/presspass/press_releases/NuTeV.html
 24

I. Kant, ``Prolegomena to any future metaphysics'', 1783.
 25

A. Einstein, ``Autobiographisches'', in ``Albert Einstein:
PhilosopherScientist'', P.A. Schilpp ed., Library of Living
Philosophers, Tudor, Evanston, Ill., 1949, pp. 295.
 26

A. Einstein,
``Über die spezielle und die allgemeine
Relativitätstheorie (gemeinverständlich)'', Vieweg, Braunschweig, 1917.
Translation: ``Relativity: the special and the general Theory.
A popular exposition'', London Methuen 1946.
 27
 J.M. Bernardo and A.F.M. Smith,
``Bayesian theory'', John Wiley & Sons, 1994.
 28

D. Hume, ``Enquiry concerning human understanding'' (1748),
see, e.g.,
http://www.utm.edu/research/hume/wri/1enq/1enq6.htm,
 29

G. D'Agostini, ``Teaching statistics in the physics curriculum.
Unifying and clarifying role of subjective probability'',
Am. J. Phys. 67 (1999) 1260 [physics/9908014].
 30

G. D'Agostini, ``Bayesian reasoning versus conventional statistics
in high energy physics'',
Proc. XVIII International Workshop
on Maximum Entropy and Bayesian Methods, Garching (Germany), July 1998,
V. Dose
et al. eds.,
Kluwer Academic Publishers, Dordrecht, 1999
[physics/9811046]
.
 31

G. D'Agostini, contribution to the panel discussion at
Workshop on Confidence Limits, Geneva, Switzerland,
January 2000, CERN Report 2000005 pp. 285286
[http://epdiv.web.cern.ch/epdiv/Events/CLW/QA/PS/clwdiscuss.ps].
 32

G. D'Agostini, ``Role and meaning of subjective probability:
some comments on common misconceptions'',
XX International Workshop
on Maximum Entropy and Bayesian Methods in Science and
Engineering, GifsurYvette (France), July 2000,
A. MohammadDjafari, ed,
AIP Conference Proceedings, Vol. 568, 2001
[physics/0010064]
 33

G. D'Agostini, ``Overcoming priors anxiety'',
Bayesian Methods in the Sciences, J. M. Bernardo Ed.,
special issue of Rev. Acad. Cien. Madrid,
Vol. 93, Num. 3, 1999
[physics/9906048].
 34

S.J. Press and J.M. Tanur, ``The subjectivity of scientists and the
Bayesian approach'', John Wiley & Sons, 2001.
 35

K. Weise, private communication, August 1995.
 36
 K. Weise, W. Wöger,
``A Bayesian theory of measurement uncertainty'',
Meas. Sci. Technol. 4 (1993) 1.
 37

H. O. Lancaster, ``The Chisquared Distribution'', John
Wiley & Sons, 1969.
 38

G. D'Agostini and G. Degrassi, ``Constraints on the Higgs boson
mass from direct searches and precision measurements'',
Eur. Phys. J. C10 (1999) 633
[hepph/9902226].
 39

P.S. Laplace, ``Théorie Analityque des Probabilités'', 1812.
 40

B. de Finetti, ``Probabilità'', entry for Enciclopedia Einaudi,
1980.
 41

E. Schrödinger, ``The foundation of the theory of probability  I'',
Proc. R. Irish Acad. 51A (1947) 51;
reprinted in Collected papers Vol. 1
(Vienna 1984: Austrian Academy of Science) 463
.
 42

R. Scozzafava, ``La probabilità soggettiva e le sue
applicazioni'', Masson, Editoriale Veschi, Roma, 1993.
 43
 A. O'Hagan, ``Bayesian Inference'', Vol.B
of Kendall's advanced theory of statistics (Halsted Press,
1994).
 44
 E.T. Jaynes, ``Information theory and statistical mechanics'',
Phys. Rev. 106 (1957) 620.
 45

R.T. Cox, ``Probability, Frequency and Reasonable Expectation''
Am. J. Phys. 14 (1946) 1.
 46

D.S. Sivia, ``Data analysis  a Bayesian tutorial'',
Clarendon Press, Oxford University Press, 1997.
 47

F.H. Fröhner ``Evaluation and Analysis of Nuclear
Resonance Data'', JEFF Report 18
(Nuclear Energy Agency and Organization for Economic Cooperation and
Development), 2000
[http://www.nea.fr/html/ dbdata/nds_jefreports/jefreport18/jeff18.pdf]
 48

M. Tribus, ``Rational descriptions, decisions and designs'',
Pergamon Press, 1969.
 49
 H. Jeffreys, ``Theory of probability'', Oxford
University Press, 1961.
 50

E. Schrödinger,
``The foundation of the theory of probability  II'',
Proc. R. Irish Acad.
51A (1947) 141;
reprinted in Collected papers Vol. 1
(Vienna 1984: Austrian Academy of Science) 479.
 51
 Particle Data Group (PDG), C. Caso et al.,
``Review of particle properties'',
Phys. Rev. D50 (1994) 1173.
 52
 New Scientist, April 28 1995, pag. 18 (``Gravitational
constant is up in the air''). The data
of Table 3.2 are from H. Meyer's DESY seminar,
June 28, 1995.
 53

P. Watzlawick, J.H. Weakland and R. Fisch,
``Change: principles of problem formation and problem resolution'',
W.W. Norton, New York, 1974.
 54

R. von Mises, ``Probability, Statistics, and Truth'',
Allen and Unwin, 1957.
 55

D.C. Knill and W. Richards (eds.), ``Perception as Bayesian Inference'',
Cambridge University Press, 1996.
 56

C. Glymour, ``Thinking things through: an introduction
to philosophical issues and achievements'', MIT Press, 1997.
 57

J.O. Berger, ``Statistical decision theory and
Bayesian analysis'', Springer, 1985.
 58

C.P. Robert, ``The Bayesian choice'', Springer, 1994.
 59

G. D'Agostini, ``Confidence limits: what is the Problem?
Is there the solution?'',
Workshop on Confidence Limits, Geneva, Switzerland,
January 2000, CERN Report 2000005
[hepex/0002055].
 60

A.L. Read, ``Modified frequentistic analysis of search results
(the CL method)'', Workshop on Confidence Limits, Geneva, Switzerland,
January 2000, CERN Report 2000005
[http://epdiv.web.cern.ch/ epdiv/Events/CLW/papers.html].
 61
 P.L. Galison, ``How experiments end'', The University of Chicago Press,
1987.
 62
 G. D'Agostini, ``Limits on electron compositeness from the
Bhabha scattering at PEP and PETRA'',
Proceedings of the
XXV Rencontre de Moriond on ``Z0 Physics'',
Les Arcs (France), March 411, 1990, p. 229 (also DESY90093).
 63
 A.K. Wróblewski, ``Arbitrariness in the development of physics'',
afterdinner talk at the International Workshop on
Deep Inelastic Scattering and Related Subjects, Eilat, Israel,
611 February 1994, Ed. A. Levy (World Scientific, 1994), p. 478.
 64
 C.E. Shannon, ``A mathematical theory of communication'',
Bell System Tech. J. 27 (1948) 379, 623. Reprinted in the
Mathematical Theory of Communication (C.E. Shannon
and W. Weaver), Univ. Illinois Press, 1949.
 65

R.E. Kalman,
``A new approach to linear filtering and prediction problems'',
Trans. ASME J. of Basic Engin. 82 (1960) 35.
 66

P.S. Maybaeck, ``Stochastic models, estimation and control'',
Vol. 1, Academic Press, 1979.
 67

G. Welch and G. Bishop>, ``An introduction to Kalman filter'', 2002
http://www.cs.unc. edu/~welch/kalman/.
 68

C.F. Gauss, ``Theoria motus corporum coelestium in sectionibus
conicis solem ambientum'', Hamburg 1809, n.i 172179; reprinted
in Werke, Vol. 7 (Gota, Göttingen, 1871), pp 225234.
 69

F. Lad, ``Operational subjective statistical methods 
a mathematical, philosophical, and historical introduction'',
J. Wiley & Sons, 1996.
 70

G. Coletti and R. Scozzafava,
``Probabilistic logic in a coherent setting'',
Kluwer Academic Publishers, 2002.
 71

T. Bayes, ``An assay towards solving a problem in the doctrine
of chances'', Phil. Trans. Roy. Soc., 53 (1763) 370
 72

P. Astone and G. Pizzella, ``Upper limits in the case that zero
events are observed: An intuitive solution to the background
dependence puzzle'',
Workshop on Confidence Limits, Geneva, Switzerland,
January 2000, CERN Report 2000005
[hepex/0002028].
 73

G.J. Feldman and R.D. Cousins, ``Unified approach to the classical
statistical analysis of small signal'', Phys. Rev. D57 (1998) 3873
[physics/9711021].
 74

J. Orear, ``Enrico Fermi, the man'',
Il Nuovo Saggiatore 17, no. 56 (2001) 30
 75

A. Gelman, J.B. Carlin, H.S. Stern and D.B. Rubin,
``Bayesian data analysis'', Chapman & Hall, 1995.
 76

D.G.T Denison, C.C. Holmes, B.K. Mallick and A.F.M. Smith,
``Bayesian methods for nonlinear classification and regression'',
Jonh Wiley and Sons, 2002.
 77

G. D'Agostini, ``Inferring rho a eta
of the CKM matrix
 A simplified, intuitive approach'',
May 2001, hepex/0107067.
 78

M. Ciuchini et al. ``2000 CKMTriangle Analysis: A critical review
with updated experimental inputs and theoretical parameters'',
JHEP 0107 (2001) 013
[hepph/0012308].
 79
 Particle Data Group (PDG), C. Caso et al.,
``Review of particle physics'', Eur. Phys. J.
C3 (1998) 1 (http://pdg.lbl.gov/).
 80
 G. D'Agostini, ``On the use of the covariance matrix to fit correlated
data'', Nucl. Instrum. Methods. A346 (1994) 306
[scanned version at KEK].
 81
 CELLO Collaboration, H.J. Behrend et al.,
``Determination of alpha_{s} and
sin^{2}(theta)
from measurements
of total hadronic cross section in annihilation'',
Phys. Lett.
183B (1987) 400.
 82

G. D'Agostini, ``Determination of alpha_{s} and
sin^{2}(theta)
from
measurements at PEP and PETRA'', Proceedings of
XXII Rencontre de Moriond on ``Hadrons, Quarks and Gluons'',
Les Arcs, France, March 1525, 1987.
 83
 S. Chiba and D.L. Smith, ``Impacts of data transformations
on leastsquare solutions and their significance in data analysis and
evaluation'',
J. Nucl. Sc. Tech. 31 (1994) 770.
 84
 M. L. Swartz, ``Reevaluation of the hadronic contribution
to alpha(M_{Z}^{2})'',
Phys. Rev. D53 (1996) 5268
[hepph/9509248].
 85
 T. Takeuchi, ``The status of the determination of
alpha_{s}(M_{Z})'',
Prog. Theor. Phys. Suppl.
123 (1996) 247
[hepph/9603415].
 86

S. Forte, J.I. Latorre, L. Magnea and A. Piccione,
``Determination of alpha_{s} from scaling violations
of truncated moments of structure functions'',
Nucl. Phys. B643 (2002) 477
[hepph/0205286].
 87
 V. Blobel, ``Unfolding methods in high energy
physics experiments'',
Proceedings of the ``1984 CERN School of Computing'',
Aiguablava, Catalonia, Spain, 912 September 1984,
Published by CERN, July 1985, pp. 88127
[OPAL Technical Note 361].
 88
 G. Zech, ``Comparing statistical data to Monte Carlo simulation 
parameter fitting and unfolding'', DESY 95113, June 1995.
 89
 G. D'Agostini, ``A multidimensional unfolding method based on
Bayes' theorem'', Nucl. Instrum. Methods A362 (1995) 487.
[scanned version at KEK].
 90
 K. Weise, ``Mathematical foundation of an analytical
approach to Bayesian Monte Carlo spectrum unfolding'',
Physicalish Technische Bundesanstalt, Braunschweig, BTBN24,
July 1995.
 91

S.F. Gull and J. Skilling,
``Quantifying Maximum Entropy'',
manual of MemSys5 package,
www.maxent.co.uk/documents_1.htm.
 92

B. Buck and V.A. Macaulay (eds.), ``Maximum Entropy in action'',
Oxford University Press, 1991.
 93

International Workshops
on Maximum Entropy and Bayesian Methods (22 editions till 2002),
proceedings often published by
Kluwer Academic Publishers.
See also http://omega.albany.edu:8008/maxent.htm
 94

K.M. Hanson,
``Introduction to Bayesian image analysis,
Medical Imaging: Image Processing
M.H. Loew ed., Proc. SPIE 1898 (1993) 716
[http://public.lanl.gov/kmh/publications/medim93.pdf].
 95

G. Polya, ``Mathematics and plausible reasoning'', Volume II:
Patterns of plausible inference, Princeton University Press, 1968.
 96

A. Franklin, "e;Experiment, right or wrong"e;,
Cambridge University Press, 1990.
 97

D.A. Berry, ``Teaching elementary Bayesian statistics with
real applications in science'',
Am. Stat. 51 (1997) 241;
J. Albert, ``Teaching Bayes' rule: a dataoriented approach'',
ibid., p. 247.
D.S. Moore, ``Bayes for beginners? Some reasons to hesitate'',
ibid., p. 254.
Pages 262272 contain five discussions plus replies.
 98

K.S. Thorne, ``Black holes and time warps: Einstein's
outrageous legacy'', W.W. Norton & Company, 1994.
 99

M. De Maria and A. Russo,
``The discovery of the positron'', Rivista di Storia della Scienza,
2 (1985) 237.
 100

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)
[hepph/9706375].
 101

See e.g. G. Altarelli, ``The status of the Standard Model'', talk at
18th International Symposium on LeptonPhoton Interactions,
Hamburg, August 1997,
CERNTH97278, Oct. 1997
[hepph/9710434].
 102

R. Feynman, ``The character of the physical law'',
The MIT Press, 1967
 103

B. Efron, ``Why isn't everyone a Bayesian?'',
Am. Stat. 40 (1986) 1, with discussion on pages 611.
 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, ``Noninformative 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. 177189.
 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
)
 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 2000005, p. 277.
[http://epdiv.web.cern.ch/epdiv/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 HighEnergy 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.
 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
[astroph/0107260>].
 117

M.V. John and J.V. Narlikar, ``Comparison of
cosmological models using Bayesian theory'',
Phys.Rev. D65 (2002) 043506
[astroph/0111122].
 118

M.P. Hobson, S.L. Bridle and O. Lahav,
``Combining cosmological datasets:
hyperparameters and Bayesian evidence'', 2002,
astroph/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/cmutalk.pdf.
 120

See, e.g, J. Pearl, ``Probabilistic reasoning in intelligent systems:
networks of plausible inference'', Morgan Kaufmann Publishers, 1988.
F.V. Jensen, ``An introduction to Bayesian networks'',
UCL Press (and Springer Verlag), 1996.
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,
``Decisiontheoretic 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.
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.
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://www2.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.mrcbsu.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
[hepex/0208009].
 127

G. D'Agostini, ``Sceptical combination of experimental results:
General considerations and application to epsilon'/epsilon'',
CERNEP/99139, October 1999,
hepex/9910036, and references therein.
 128

M. Fabbrichesi, ``Estimating epsilon'/epsilon.
A user's manual'',
Nucl. Phys. Proc. Suppl. 86 (2000) 322
[hepph/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, 2729 Apr 1995
[astroph/9604126].
 131

C. Pascaud and F. Zomer,
``QCD analysis from the proton structure function measurement:
issues on fitting, statistical and systematic errors'',
LAL 9505, June 1995
[http://wwwh1.desy.de/h1work/fit/ h1fit.info.html].
 132

S. Alekhin,
``Extraction of parton distributions and alpha_{s}
from DIS
data within the Bayesian treatment of systematic errors'',
Eur. Phys. J. C10 (1999) 395
[hepph/9611213].
 133

M. Botje,
``A QCD analysis of HERA and fixed target
structure function data'', ZEUS Note 98062
DESY99038, December 1999
[hepph/9912439].
 134

R.S. Thorne et al.
``Questions on uncertainties in parton distributions'',
Conference on Advanced Statistical Techniques in Particle Physics,
March 2002, Durham,
hepph/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'',
CERNEP/2000026, February 2000
[hepex/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)'',
CERNEP/99126, August 1999
[hepex/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
[astroph/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.,
SpringerVerlag (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
[hepex/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, 1718 January 2000
[hepph/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).
 145

J. Earman, ``Bayes or bust? A critical examination of Bayesian
confirmation theory'', The MIT Press, 1992.
 146

R. Jeffrey, ``Probabilistic thinking'', 1995,
http://www.princeton.edu/bayesway/ProbThink/
 147

M. Kaplan, ``Decision theory as philosophy'', Cambridge University
Press, 1996.
 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.
 151

B. de Finetti, ``Filosofia della probabilità'',
il Saggiatore, 1995.
 152

L. Piccinato, ``Metodi per le decisioni statistiche'', SpringerItalia,
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.
 155
 S. J. Press,
``Bayesian statistics: principles, models, and applications'',
John Wiley & Sons, 1989.
 156

G.E.P. Box and G.C. Tiao, ``Bayesian inference in
statistical analysis'', John Wiley and Sons, 1973.
 157

A. O'Hagan, ``Probability: methods and measurements'',
Chapman & Hall, 1988.
 158

P.M. Lee, ``Bayesian statistics  an introduction'',
John Wiley and Sons, 1997.
 159

L.J. Savage et al., ``The foundations of statistical inference:
a discussion'', Methuen, 1962.
 160

A. Zellner, ``Bayesian analysis in econometrics and statistics'',
Eduard Elgar, 1997.
 161

J.M. Bernardo et al., Valencia Meetings on ``Bayesian Statistics'' 17,
http://www.uv.es/bernardo/valenciam.html.
Latest issues:
7 ;
6 ;
5
 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,
ChapmanHall.
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.artiste.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 CRGTR931, 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.
 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, GifsurYvette (France),
July 2000,
 173

A. Lewis and S. Bridle,
``Cosmological parameters from CMB and other data:
a MonteCarlo approach'',
Phys. Rev. D66 (2002) 103511
[astroph/0205436].
 174

http://cerebro.xu.edu/math/Sources/.
 Top  CONTENTS 
hypertexted BIBLIOGRAPHY 
INDEX 
ERRATA  Book reviews 
Author Home Page 
Index
"Delta chi^2 = 1" rule, 170, 269271
"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, 6365, 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, 148150
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 INC1, 31
black hole, 218
blending factor, 126
bound
probabilistic, 299, 301
sensitivity, 299, 301
branching ratio, 141
CELLO, 199
central limit theorem, 110113, 183, 187
terms, 108
chisquare
$Delta \chi^2 = 1$ rule, 170, 269271
distribution, 96
minimization (fit), 170, 269271
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, 158162
sceptical combination, 252254
combinatorial `definition' of probability, 30
complete class, 58
conditional inference, 44
conditional probability, 6062, 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, 179181, 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, 229231, 301
Cox R.T., 57
credibility interval, 124
cumulative function, 90, 93
Cygnus X1, 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
doghunter, 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, 172174
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, 137139, 172
Gaussian
distribution, 94
distribution of error, 112
Gauss derivation, 137139
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
hunterdog, 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, 290293
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, 172174
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
noninformative priors, 223
normal, see {Gaussian}{94}
null hypothesis, 15
null observation, 154
objective Bayesian theory, 222
objective inference, 223
objectivity of physics, 216218
Ockham' Razor, 239, 240
odds in betting, 54
operational subjectivism, 225
Orear J., 171
outliers, 247
output quantity, 273
pvalue, 16
Particle Data Group (PDG), 213, 221, 248, 259, 260, 268, 269
particle identification, 66
Pauli W., 51
Pearson chisquare, 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, 3638, 40, 65, 120, 125, 126
conjugate, 126
logical necessity, 37, 238
motivated by `positive attitude', 131
noninformative, 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, 6062
density function, 32, 92
distribution
beta, 97
binomial, 91
bivariate Gaussian, 101
chisquare, 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, 104108, 191
linearization, 178181, 276278
nonmonotonic 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, 178181
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, 57
probability of, 9
type A uncertainty, 133, 181
type B uncertainty, 133, 181184, 186
uncertain numbers, 31, 89
uncertainty, 4, 5, 115, 116
`standard' treatment, 7
asymmetric, 267
propagation, 8, 42, 44, 104108, 191, 268
source, 3
sources (ISO), 6
uncertainty and probability, 29
unfolding, 203206, 208
uniform distribution, 94
upper limit
binomial model, 145
Poisson model, 154, 157164, 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):
 In denominator of Eq. (8.20) the average of x should be squared.
Book reviews
 Journal of the American Statistical Association (by G. Woodworth),
2004, vol. 99, no. 468, pp. 1201  1202
"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 upperlevel 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"
 Top
 CONTENTS 
hypertexted BIBLIOGRAPHY 
INDEX 
ERRATA  Book reviews 
Author Home Page 