Bibliography

1

G. D'Agostini and A. Esposito, Checking individuals and sampling populations with imperfect tests, arXiv:2009.04843 [q-bio.PE].

2

W. Nelson, Confidence intervals for the ratio of two Poisson means and Poisson predictor intervals, IEEE Trans. on Reliability, Vol. R-19 (1970) 42-49.

3

F. James and M Roos, Errors on ratios of small numbers of events, Nuclear Physics B172 (1980) 475-470.

4

K.J. Coakley, D.S. Simons and A.M. Leifer, Secondary ion mass spectroscopy measurements in isotopic ratios: corrections for time varying count rate, Int. J. of Mass Spectrometry 240 (2005) 107-120.

5

K. Gu, H.K.T. Ng, M.L. Tang and W.R. Schucany, Testing the ratio of two Poisson rates, Biometrical Journal 50 (2008) 283-298.

6

R.C. Ogliore, G.R. Huss and K. Nagashima, Ratio estimation in SIMS analysis, Nucl. Instr. and Meth, in Phys. Reas. B269 (2011) 1910-1918.

7

C.D. Coath, R.C.J. Steele and W.F. Lunnon, Statistical bias in isotope ratios, J. Anal. At. Spectrom., 2013, 28, 52-58.

8

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, arXiv:physics/9906048 [physics.data-an].

9

International Organization for Standardization (ISO), Guide to the expression of uncertainty in measurement, Geneva, Switzerland, 1993.

10

https://en.wikipedia.org/wiki/Skellam_distribution .

11

R Core Team (2018), R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
https://www.R-project.org/ .

12

J.W. Lewis et al., Package ‘skellam’,
https://CRAN.R-project.org/package=skellam .

13

G. D'Agostini, Bayesian Reasoning in Data Analysis. A critical Introduction, World Scientific, 2003.

14

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, arXiv:physics/9811046 [physics.data-an].

15

G. D'Agostini, The Waves and the Sigmas (To Say Nothing of the 750 GeV Mirage), arXiv:1609.01668 [physics.data-an].

16

D. Hume, Enquiry concerning human understanding (1748)
LibriVox entry (Chapter 8: Of probability)

17

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, arXiv:hep-ex/9909047 .

18

J. Pearl, Causality, Cambridge University Press, 2000.

19

Bayes, Thomas and Price, Richard An Essay towards solving a Problem in the Doctrine of Chance. By the late Rev. Mr. Bayes, communicated by Mr. Price, in a letter to John Canton, A.M.F.R.S., Philosophical Transactions of the Royal Society of London. 53: 370–418, (1763), https://doi.org/10.1098

20

P.S. Laplace, Mémoire sur la probabilité des causes par les événements”, Mémoire de l'Académie royale des Sciences de Paris (Savants étrangers), Tome VI, p. 621, 1774, https://gallica.bnf.fr/ark:/12148/bpt6k77596b/f32 .

21

H. Poincaré, “Science and Hypothesis”, 1905 (Dover Publications, 1952).

22

M.G. Kendal and A. Stuart, The advanced theory of statistics, 1943 (C. Griffin & Co., 1969).

23

G. D'Agostini and G. Degrassi, Constraints on the Higgs boson mass from direct searches and precision measurements, Eur. Phys. J. C10 (1999) 633, https://arxiv.org/abs/hep-ph/9902226 .

24

S. Gariazzo, Constraining power of open likelihoods, made prior-independent, arXiv:1910.06646 [astro-ph.CO] .

25

P.F. de Salas, D.V. Forero, S. Gariazzo, P. Martínez-Miravé, O. Mena, C.A. Ternes, M. Tórtola, J.W.F. Valle, 2020 Global reassessment of the neutrino oscillation picture, arXiv:2006.11237 [hep-ph] .

26

G. Grilli di Cortona, A. Andrea and S. Piacentini, Migdal effect and photon Bremsstrahlung: improving the sensitivity to light dark matter of liquid argon experiments, arXiv:2006.02453 [hep-ph] .

27

G. D'Agostini, Confidence limits: what is the problem? Is there the solution?, Workshop on Confidence Limits, CERN, Geneva, 17-18 January 2000,
arXiv:hep-ex/0002055.

28

C.F. Gauss, Theoria motus corporum coelestium in sectionibus conicis solem ambientum, Hamburg 1809,
https://archive.org/details/bub_gb_ORUOAAAAQAAJ .

29

G. D'Agostini, Skeptical combination of experimental results using JAGS/rjags with application to the K$^\pm$ mass determination,
arXiv:2001.03466 [physics.data-an]

30

https://en.wikipedia.org/wiki/Conjugate_prior .

31

M. Bognar, Probability distributions,
https://play.google.com/store/apps/details?id=com.mbognar.probdist,
https://apps.apple.com/us/app/probability-distributions/id889106396 .

32

https://en.wikipedia.org/wiki/Gamma_distribution .

33

https://en.wikipedia.org/wiki/Beta_function .

34

https://en.wikipedia.org/wiki/Beta_prime_distribution .

35

Th. Cathcart and D. Klein, Plato and a Platypus walk into a bar...: understanding Philosophy through jokes, Penguin Group, 2008.

36

M. Plummer, JAGS: A Program for Analysis of Bayesian Graphical Models Using Gibbs Sampling, Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003), March 20–22, Vienna, Austria. ISSN 1609-395X, http://mcmc-jags.sourceforge.net/ .

37

M. Plummer, rjags: Bayesian Graphical Models using MCMC.
R package version 4-10, https://CRAN.R-project.org/package=rjags .

38

C. Andrieu et al., An introduction to MCMC for Machine Learning, Machine Learning 50 5-43 (2003), https://doi.org/10.1023/A:1020281327116 .

39

D. Lunn et al., The BUGS project: Evolution, critique and future directions, Statistics in Medicine 28 3049-3067 (2008),
https://doi.org/10.1002/sim.3680 .

40

The BUGS Project, http://www.mrc-bsu.cam.ac.uk/software/bugs/ .

41

http://www.openbugs.net/w/Examples .

42

J.O. Berger and D.A. Berry, Statistical analysis and the illusion of objectivity, Am. Scientist 76 (1988) 159.

43

G. D'Agostini, Fits, and especially linear fits, with errors on both axes, extra variance of the data points and other complications,
arXiv:physics/0511182 [physics.data-an] .

44

G. D'Agostini, On a curious bias arising when the $\chi^2/\nu$ scaling prescription is first applied to a sub-sample of the individual results,
arXiv:2001.07562 [physics.data-an] .

45

A. Caldwell et al., BAT: The Bayesian Analysis Toolkit,
Comput. Phys. Comm. 180 (2009) 2197-2209;
J.Phys.Conf.Ser. 219 (2010) 032013;
J.Phys.Conf.Ser. 331 (2011) 072040;
https://bat.mpp.mpg.de/ .

46

J. Bezanson, A. Edelman, S. Karpinski, V.B. Shah, Julia: A Fresh Approach to Numerical Computing,
arXiv:1411.1607 [cs.MS]

47

O. Schulz et al. BAT.jl - A Julia-based tool for Bayesian inference,
arXiv:2008.03132 [stat.CO].