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This is a writeup of lectures on "statistics" that have evolved from the initial version for the 2009 Hadron Collider Physics Summer School at CERN to versions for other venues and, most recently, for the African School of Fundamental Physics and Applications in 2024.
E. B. Wilson, “Probable Inference, the Law of Succession, and Statistical Inference”, J. Amer. Stat. Assoc
1927
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C. J. Clopper and E. S. Pearson, “The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial”, Biometrika
1934
Earlier work this paper cites.
F. Garwood, “Fiducial Limits for the Poisson Distribution”, Biometrika
1936
Earlier work this paper cites.
J. Neyman, “Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability”, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
1937
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E. S. Pearson, “The Probability Integral Transformation for Testing Goodness of Fit and Combining Independent Tests of Significance”, Biometrika
1938
Earlier work this paper cites.
S. S. Wilks, “The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses”, Ann. Math. Stat
1938
Earlier work this paper cites.
B. L. Welch, “On Confidence Limits and Sufficiency, with Particular Reference to Parameters of Location”, Annals Math. Stat
1939
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Dover Books on Mathematics Series. Dover Publications, New York, 2nd edition, 1972
L. J. Savage, “The Foundations of Statistics” · 1954
Earlier work this paper cites.
D. R. Cox, “Some Problems Connected with Statistical Inference”, Annals Math. Stat
1958
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R. J. Buehler, “Some Validity Criteria for Statistical Inferences”, Annals Math. Stat
1959
Earlier work this paper cites.
Oxford University Press, Oxford, 3rd edition, 1961
H. Jeffreys, “Theory of Probability” · 1961
Earlier work this paper cites.
A. Birnbaum, “On the Foundations of Statistical Inference: Binary Experiments”, Annals Math. Stat
1961
Earlier work this paper cites.
Methuen & Co. (also Wiley), London (also New York), 1962
G. Barnard and D. Cox, “The Foundations of Statistical Inference: A Discussion” · 1962
Earlier work this paper cites.
B. L. Welch and H. W. Peers, “On Formulae for Confidence Points Based on Integrals of Weighted Likelihoods”, J. Royal Stat. Soc. Series B (Methodological)
1963
Earlier work this paper cites.
Wiley, U.K., 2017
B. de Finetti, “Theory of Probability: A Critical Introductory Treatment” · 1970
Earlier work this paper cites.
A. Birnbaum, “The Neyman-Pearson Theory as Decision Theory, and as Inference Theory; With a Criticism of the Lindley-Savage Argument for Bayesian Theory”, Synthese
1977
Earlier work this paper cites.
G. Schwarz, “Estimating the Dimension of a Model”, The Annals of Statistics
1978
Earlier work this paper cites.
J. M. Bernardo, “Reference Posterior Distributions for Bayesian Inference”, J. Royal Stat. Soc. Series B (Methodological)
1979
Earlier work this paper cites.
F. James and M. Roos, “Errors on Ratios of Small Numbers of Events”, Nucl. Phys. B
1980
Earlier work this paper cites.
F. James, “Interpretation of the Shape of the Likelihood Function around Its Minimum”, Comput. Phys. Commun
1980
Earlier work this paper cites.
S. Baker and R. D. Cousins, “Clarification of the Use of Chi-Square and Likelihood Functions in Fits to Histograms”, Nucl. Instrum. Meth
1984
Earlier work this paper cites.
Springer Series in Statistics. Springer, New York, 2nd edition, 1985
J. O. Berger, “Statistical Decision Theory and Bayesian Analysis” · 1985
Earlier work this paper cites.
Marcel Dekker, Inc., New York, 1986
R. B. D’Agostino and M. A. Stephens, eds., “Goodness-of-fit Techniques” · 1986
Earlier work this paper cites.
J. O. Berger and R. L. Wolpert, “The Likelihood Principle”, Institute of Mathematical Statistics Lecture Notes–Monograph Series
1988
Earlier work this paper cites.
Wiley, Chichester, U.K, 1989
R. J. Barlow, “Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences” · 1989
Earlier work this paper cites.
J. O. Berger and J. M. Bernardo, “Estimating a Product of Means: Bayesian Analysis with Reference Priors”, J. Amer. Stat. Assoc
1989
Earlier work this paper cites.
G. Zech, “Upper Limits in Experiments with Background or Measurement Errors”, Nucl. Instrum. Meth. A
1989
Earlier work this paper cites.
D. V. Lindley, “[The 1988 Wald Memorial Lectures: The Present Position in Bayesian Statistics]: Rejoinder”, Statist. Sci
1990
Earlier work this paper cites.
J. O. Berger and J. M. Bernardo, “Ordered Group Reference Priors with Application to the Multinomial Problem”, Biometrika
1992
Earlier work this paper cites.
R. D. Cousins and V. L. Highland, “Incorporating systematic uncertainties into an upper limit”, Nucl. Instrum. Meth. A
1992
Earlier work this paper cites.
E. L. Lehmann, “The Fisher, Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?”, J. Amer. Stat. Assoc
1993
Earlier work this paper cites.
R. D. Cousins, “Why isn’t every physicist a Bayesian?”, Amer. J. Phys
1995
Earlier work this paper cites.
R. E. Kass and L. Wasserman, “The Selection of Prior Distributions by Formal Rules”, J. Amer. Stat. Assoc
1996
Earlier work this paper cites.
Oxford University Press, New York, 1996
J. Lindsey, “Parametric Statistical Inference” · 1996
Earlier work this paper cites.
T. Z. Irony and N. D. Singpurwalla, “Non-informative priors do not exist: A dialogue with José M. Bernardo”, J. Statistical Planning and Inference
1997
Earlier work this paper cites.
R. Brun and F. Rademakers, “ROOT: An object oriented data analysis framework”, Nucl. Instrum. Meth. A
1997
Earlier work this paper cites.
Clarendon Press, Oxford, 1998
G. Cowan, “Statistical Data Analysis” · 1998
Earlier work this paper cites.
G. J. Feldman and R. D. Cousins, “Unified Approach to the Classical Statistical Analysis of Small Signals”, Phys. Rev. D
1998
Earlier work this paper cites.
Arnold, London, 6th edition, 1999
A. Stuart, K. Ord, and S. Arnold, “Kendall’s Advanced Theory of Statistics”, volume 2A · 1999
Earlier work this paper cites.
KARMEN Collaboration, “The Search for Neutrino Oscillations ν ¯ μ → ν ¯ e \bar{\nu}_{\mu}\rightarrow\bar{\nu}_{e} with KARMEN”, Nucl. Phys. Proc. Suppl
1999
Earlier work this paper cites.
T. Junk, “Confidence level computation for combining searches with small statistics”, Nucl. Instrum. Meth. A
1999
Earlier work this paper cites.
D. V. Lindley, “The Philosophy of Statistics”, J. Royal Stat. Soc. Series D (The Statistician)
2000
Earlier work this paper cites.
J. Berger, “Convergence of objective Bayesian and frequentist methodology for confidence limits”,. Talk at Workshop on Confidence Limits, Fermilab, 27-28 March 2000. The hand-written slides are still a good read, concluding with “Objective Bayesian analysis is the best frequentist tool around.” http://conferences.fnal.gov/cl2k/
2000
Earlier work this paper cites.
CDF Collaboration, “A measurement of sin ( 2 β ) \sin(2\beta) from B → J / ψ K S 0 B\to J/\psi K^{0}_{S} with the CDF detector”, Phys. Rev. D
2000
Cited alongside, same era.
Oxford science publications. Oxford University Press, Oxford, 2000
T. Severini, “Likelihood Methods in Statistics” · 2000
Cited alongside, same era.
W. Rolke, “Confidence intervals and upper bounds for small signals in the presence of noise”, (2000). Talk at Workshop on Confidence Limits, Fermilab, 27-28 March 2000. http://conferences.fnal.gov/cl2k/
2000
Cited alongside, same era.
Inst. of Mathematical Statistics, Beachwood, Ohio, 2001
J. Berger and L. Pericchi, “Objective Bayesian Methods for Model Selection: Introduction and Comparison”, in Model Selection · 2001
Cited alongside, same era.
J. G. Heinrich, “The Log Likelihood Ratio of the Poisson Distribution for Small μ \mu ”, (2001). http://www-cdf.fnal.gov/physics/statistics/notes/cdf5718_loglikeratv2.ps.gz
L. Moneta, K. Belasco, K. S. Cranmer et al., “The RooStats Project”, PoS
2010
Later among the works it cites.
Springer Science+Business Media, New York, 2010
O. Thas, “Comparing Distributions” · 2010
Later among the works it cites.
2010
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http://www.physics.ox.ac.uk/Users/lyons/LEE_feb7_2010.pdf
L. Lyons, “Comments on ‘Look Elsewhere Effect’ ”, 2010 · 2010
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2010
Later among the works it cites.
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2001
Cited alongside, same era.
Brooks/Cole, Cengage Learning, Belmont, CA, 2nd edition, 2002
G. Casella and R. L. Berger, “Statistical Inference” · 2002
Cited alongside, same era.
J. Neyman and E. S. Pearson, “On the Problem of the Most Efficient Tests of Statistical Hypotheses”, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character
2002
Cited alongside, same era.
A. L. Read, “Presentation of search results: The CL s {}_{\text{s}} technique”, J. Phys. G
2002
Cited alongside, same era.
B. Aslan and G. Zech, “A new class of binning free, multivariate goodness-of-fit tests: the energy tests”, (2002). arXiv:hep-ex/0203010
2002
Cited alongside, same era.
SLAC eConf C030908, 2003
B. Efron, “Bayesians, Frequentists, and Physicists”, in Proceedings of PHYSTAT 2003: Statistical problems in particle physics, astrophysics and cosmology, Stanford, USA, September 8-11, 2003 · 2003
Cited alongside, same era.
Cambridge University Press, Cambridge, U.K., 2003
E. Jaynes, “Probability Theory: The Logic of Science” · 2003
Cited alongside, same era.
J. O. Berger, “Could Fisher, Jeffreys and Neyman Have Agreed on Testing?”, Statist. Sci
2003
Cited alongside, same era.
R. D. Cousins, “Bayes, Fisher, Neyman, Neutrino Masses, and the LHC”, (2011). http://www.physics.ucla.edu/~cousins/stats/cousins_bounded_gaussian_virtual_talk_12sep2011.pdf
2011
Later among the works it cites.
J. S. Conway, “Incorporating Nuisance Parameters in Likelihoods for Multisource Spectra”, (2011). Talk at PHYSTAT 2011 Workshop, CERN, Geneva, Switzerland, 17-20 January 2011. http://indico.cern.ch/event/phystat2011
2011
Later among the works it cites.
http://cdsweb.cern.ch/record/1379837
ATLAS and CMS Collaborations, LHC Higgs Combination Group, “Procedure for the LHC Higgs boson search combination in Summer 2011”, CMS/ATLAS joint note ATL-PHYS-PUB-2011-11, CMS NOTE 2011/005, (2011) · 2011
Later among the works it cites.
Talk at Progress on Statistical Issues in Searches: A Conference Involving Statistical Issues in Astrophysics, Particle Physics and Photon Science
L. Demortier, “The Parametric Bootstrap and Particle Physics”, 2012 · 2012
Later among the works it cites.
ROOT Collaboration, “HistFactory: A tool for creating statistical models for use with RooFit and RooStats”, (2012)
2012
Later among the works it cites.
J. Incandela and F. Gianotti, “Latest update in the search for the Higgs boson”, (2012). Public seminar at CERN. Video: http://cds.cern.ch/record/1459565
2012
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Wiley-VCH, Weinheim, Germany, 2013
O. Behnke, K. Kröninger, T. Schörner-Sadenius et al., eds., “Data analysis in high energy physics” · 2013
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L. Lyons, “Discovering the Significance of 5 sigma”, (2013). arXiv:1310.1284
2013
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2013
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2013
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2014
Later among the works it cites.
D. G. Mayo, “On the Birnbaum Argument for the Strong Likelihood Principle”, Statist. Sci
2014
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L. Lyons, “Raster scan or 2-D approach?”, (2014). arXiv:1404.7395 [hep-ex]
2014
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2015
Later among the works it cites.
2015
Later among the works it cites.
B. Cousins, “Physicist’s Conference Summary”,. Talk at PhyStat- ν \nu Workshop on Statistical Issues in Experimental Neutrino Physics, Kavli Inst., Kashiwa, Japan, 30 May – 1 June (2016). https://indico.ipmu.jp/indico/event/82/
2016
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R. D. Cousins, “On Goodness-of-Fit Tests”, (2016). http://cousins.web.cern.ch/cousins/ongoodness6march2016.pdf
2016
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2016
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2017
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2017
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Princeton University Press, Princeton, 2018
P. Diaconis and B. Skyrms, “Ten Great Ideas about Chance” · 2018
Closest in time.
J. C. Pezzullo, “Exact Binomial and Poisson Confidence Intervals”, (accessed 2018). http://statpages.org/confint.html
2018
Closest in time.
L. Lyons and N. Wardle, “Statistical issues in searches for new phenomena in High Energy Physics”, Journal of Physics G: Nuclear and Particle Physics
2018
Closest in time.
I. Volobouev and A. A. Trindade, “Improved inference for the signal significance”, JINST
2018
Closest in time.
L. Heinrich, M. Feickert, G. Stark et al., “pyhf: pure-Python implementation of HistFactory statistical models”, J. Open Source Softw
2021
Closest in time.
K. Cranmer and A. Held, “Building and steering binned template fits with cabinetry”, EPJ Web Conf
2021
Closest in time.
Marrakesh, Morocco, 2024, https://africanschoolofphysics.org/2023/06/28/asp2024/
“The 8th African School of Fundamental Physics and Applications, ASP2024” · 2023
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2023
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X. Zhang, S. Algeri, V. Kashyap et al., “A novel approach to detect line emission under high background in high-resolution X-ray spectra”, Monthly Notices Roy. Astr. Soc
2023
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2023
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http://www.physics.ucla.edu/~cousins/stats/theoryslides
R. Cousins, “Statistics in Theory: Prelude to Statistics in Practice”, 2024 · 2024
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Particle Data Group, S. Navas, et al., “Review of Particle Physics”, Phys. Rev. D
2024
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World Scientific, Singapore, 2024
J. O. Berger, J. M. Bernardo, and D. Sun, “Objective Bayesian Inference” · 2024
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https://scikit-learn.org/stable/
“Receiver operating characteristic” · 2024
Closest in time.
https://en.wikipedia.org/wiki/Receiver_operating_characteristic
“scikit-learn: Machine Learning in Python” · 2024
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2024
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