78
D. Krpelík and T. Basu
5. M. Beer, S. Ferson, V. Kreinovich, Imprecise probabilities in engineering analyses. Mech.
Syst. Signal Process. 37, 4–29 (2013)
6. J.O. Berger et al., An overview of robust bayesian analysis. Test 3, 5–124 (1994)
7. K.P.S. Bhaskara Rao, M.B. Rao, Theory of Charges: A Study of Finitely Additive Measures.
Pure and Applied Mathematics (Elsevier Science, Amsterdam, 1983)
8. G. Boole, An Investigation of the Laws of Thought: On Which Are Founded Mathematical
Theories of Logic and Probabilities (Dover, New York, 1854)
9. G. Casella, R.L. Berger, Statistical Inference (Thomson Learning, Pacific Grove, 2002, 2010)
10. G. Choquet, Theory of capacities: research on modern potential theory and Dirichlet problem.
Technical note, University of Kansas, Dept. of Mathematics, 1954
11. F.P.A. Coolen, Low structure imprecise predictive inference for Bayes’ problem. Stat. Probab.
Lett. 36, 349–357 (1998)
12. G. de Cooman, Possibility theory I: the measure- and integral-theoretic groundwork. Int. J.
Gen. Syst. 25, 291–323 (1997)
13. G. de Cooman, M.C.M. Troffaes, E. Miranda, A unifying approach to integration for bounded
positive charges. J. Math. Anal. Appl. 340, 982–999 (2008)
14. B. de Finetti, La Prévision: Ses Lois Logiques, Ses Sources Subjectives. Ann. Inst. Henri
Poincaré 17, 1–68 (1937)
15. B. de Finetti, Theory of Probability: A Critical Introductory Treatment (Wiley, New York,
2017)
16. A.P. Dempster, Upper and lower probabilities induced by a multivalued mapping. Ann. Math.
Stat. 38, 325–339 (1967)
17. A.P. Dempster, New methods for reasoning towards posterior distributions based on sample
data. Ann. Math. Stat. 37, 355–374 (1996)
18. A.P. Dempster, The Dempster–Shafer calculus for statisticians. Int. J. Approx. Reason. 48,
365–377 (2008)
19. D. Denneberg, Non-Additive Measure and Integral (Springer, Dordrecht, 1994)
20. S. Ferson et al., Constructing probability boxes and Dempster-Shafer structures. Tech. rep.,
Sandia National Laboratories, 2003
21. S. Ferson et al., Dependence in probabilistic modeling, Dempster–Shafer theory, and
probability bounds analysis. Tech. rep., Sandia National Laboratories, 2004
22. T. Fetz, M. Oberguggenberger, Propagation of uncertainty through multivariate functions in
the framework of sets of probability measures. Reliab. Eng. Syst. Saf. 85, 73–87 (2004)
23. R.A. Fisher, Inverse probability. Math. Proc. Camb. Philos. Soc. 26, 528–535 (1930)
24. D.A.S. Fraser, The Structure of Inference (Wiley, New York, 1968)
25. P.J. Huber, E.M. Ronchetti, Robust Statistics (Wiley, New York, 2009)
26. E.T. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press,
Cambridge, 2003)
27. A.N. Kolmogorov, Foundations of the Theory of Probability (AMS Chelsea Publication, New
York, 1956)
28. D.P. Kroese, T. Taimre, Z.I. Botev, Handbook of Monte Carlo Methods (Wiley, New York,
2011)
29. R. Martin, C. Liu, Inferential Models: Reasoning with Uncertainty (Chapman and Hall/CRC,
Boca Raton, 2015)
30. G. Matheron, Random Sets and Integral Geometry (Wiley, New York, 1975)
31. I. Molchanov, Theory of Random Sets (Springer, London, 2005)
32. R.F. Nau, De Finetti was right: probability does not exist. Theory Decis. 51, 89–124 (2001)
33. H.T. Nguyen, An Introduction to Random Sets (Chapman and Hall/CRC, Boca Raton, 2006)
34. M. Oberguggenberger, W. Fellin, Reliability bounds through random sets: non-parametric
methods and geotechnical applications. Comput. Struct. 86, 1093–1101 (2008)
35. L.J. Savage, The Foundations of Statistics (Dover, New York, 2012)
36. J.G. Saw, M.C.K. Yang, T.C. Mo, Chebyshev inequality with estimated mean and variance.
Am. Stat. 38, 130–132 (1984)
37. G. Shafer, A Mathematical Theory of Evidence (Princeton University Press, Princeton, 1976)
D. Krpelík and T. Basu
5. M. Beer, S. Ferson, V. Kreinovich, Imprecise probabilities in engineering analyses. Mech.
Syst. Signal Process. 37, 4–29 (2013)
6. J.O. Berger et al., An overview of robust bayesian analysis. Test 3, 5–124 (1994)
7. K.P.S. Bhaskara Rao, M.B. Rao, Theory of Charges: A Study of Finitely Additive Measures.
Pure and Applied Mathematics (Elsevier Science, Amsterdam, 1983)
8. G. Boole, An Investigation of the Laws of Thought: On Which Are Founded Mathematical
Theories of Logic and Probabilities (Dover, New York, 1854)
9. G. Casella, R.L. Berger, Statistical Inference (Thomson Learning, Pacific Grove, 2002, 2010)
10. G. Choquet, Theory of capacities: research on modern potential theory and Dirichlet problem.
Technical note, University of Kansas, Dept. of Mathematics, 1954
11. F.P.A. Coolen, Low structure imprecise predictive inference for Bayes’ problem. Stat. Probab.
Lett. 36, 349–357 (1998)
12. G. de Cooman, Possibility theory I: the measure- and integral-theoretic groundwork. Int. J.
Gen. Syst. 25, 291–323 (1997)
13. G. de Cooman, M.C.M. Troffaes, E. Miranda, A unifying approach to integration for bounded
positive charges. J. Math. Anal. Appl. 340, 982–999 (2008)
14. B. de Finetti, La Prévision: Ses Lois Logiques, Ses Sources Subjectives. Ann. Inst. Henri
Poincaré 17, 1–68 (1937)
15. B. de Finetti, Theory of Probability: A Critical Introductory Treatment (Wiley, New York,
2017)
16. A.P. Dempster, Upper and lower probabilities induced by a multivalued mapping. Ann. Math.
Stat. 38, 325–339 (1967)
17. A.P. Dempster, New methods for reasoning towards posterior distributions based on sample
data. Ann. Math. Stat. 37, 355–374 (1996)
18. A.P. Dempster, The Dempster–Shafer calculus for statisticians. Int. J. Approx. Reason. 48,
365–377 (2008)
19. D. Denneberg, Non-Additive Measure and Integral (Springer, Dordrecht, 1994)
20. S. Ferson et al., Constructing probability boxes and Dempster-Shafer structures. Tech. rep.,
Sandia National Laboratories, 2003
21. S. Ferson et al., Dependence in probabilistic modeling, Dempster–Shafer theory, and
probability bounds analysis. Tech. rep., Sandia National Laboratories, 2004
22. T. Fetz, M. Oberguggenberger, Propagation of uncertainty through multivariate functions in
the framework of sets of probability measures. Reliab. Eng. Syst. Saf. 85, 73–87 (2004)
23. R.A. Fisher, Inverse probability. Math. Proc. Camb. Philos. Soc. 26, 528–535 (1930)
24. D.A.S. Fraser, The Structure of Inference (Wiley, New York, 1968)
25. P.J. Huber, E.M. Ronchetti, Robust Statistics (Wiley, New York, 2009)
26. E.T. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press,
Cambridge, 2003)
27. A.N. Kolmogorov, Foundations of the Theory of Probability (AMS Chelsea Publication, New
York, 1956)
28. D.P. Kroese, T. Taimre, Z.I. Botev, Handbook of Monte Carlo Methods (Wiley, New York,
2011)
29. R. Martin, C. Liu, Inferential Models: Reasoning with Uncertainty (Chapman and Hall/CRC,
Boca Raton, 2015)
30. G. Matheron, Random Sets and Integral Geometry (Wiley, New York, 1975)
31. I. Molchanov, Theory of Random Sets (Springer, London, 2005)
32. R.F. Nau, De Finetti was right: probability does not exist. Theory Decis. 51, 89–124 (2001)
33. H.T. Nguyen, An Introduction to Random Sets (Chapman and Hall/CRC, Boca Raton, 2006)
34. M. Oberguggenberger, W. Fellin, Reliability bounds through random sets: non-parametric
methods and geotechnical applications. Comput. Struct. 86, 1093–1101 (2008)
35. L.J. Savage, The Foundations of Statistics (Dover, New York, 2012)
36. J.G. Saw, M.C.K. Yang, T.C. Mo, Chebyshev inequality with estimated mean and variance.
Am. Stat. 38, 130–132 (1984)
37. G. Shafer, A Mathematical Theory of Evidence (Princeton University Press, Princeton, 1976)