Bibliography

1

Edwin T Jaynes. Probability theory: The logic of science. Cambridge University Press, 2003.

2

Silvia Tolo, Xiange Tian, Nils Bausch, Victor Becerra, TV Santhosh, Gopika Vinod, and Edoardo Patelli. Robust on-line diagnosis tool for the early accident detection in nuclear power plants. Reliability Engineering & System Safety, 186:110–119, 2019. doi:10.1016/j.ress.2019.02.015.

3

L Zadeh. On the validity of dempster’s rule of combination, memo m 79/24. Univ. of California, Berkeley, 1979.

4

Simon Maskell. A Bayesian approach to fusing uncertain, imprecise and conflicting information. Information Fusion, 9(2):259–277, 2008. doi:10.1016/j.inffus.2007.02.003.

5

Michael S Balch. A corrector for probability dilution in satellite conjunction analysis. In 18th AIAA Non-Deterministic Approaches Conference, 1445. 2016. doi:10.2514/6.2016-1445.

6

Michael Scott Balch, Ryan Martin, and Scott Ferson. Satellite conjunction analysis and the false confidence theorem. Proceedings of the Royal Society A, 475(2227):20180565, 2019. doi:10.1098/rspa.2018.0565.

7

Andrew Gelman, Hal S Stern, John B Carlin, David B Dunson, Aki Vehtari, and Donald B Rubin. Bayesian data analysis. Chapman and Hall/CRC, 2013. doi:10.1201/b16018.

8

Albert Tarantola. Inverse problem theory and methods for model parameter estimation. Volume 89. SIAM, 2005. doi:10.1137/1.9780898717921.

9

Jerome Friedman, Trevor Hastie, and Robert Tibshirani. The elements of statistical learning. Volume 1. Springer series in statistics New York, 2001. doi:10.1007/BF02985802.

10

PL Green and Simon Maskell. Estimating the parameters of dynamical systems from big data using sequential monte carlo samplers. Mechanical Systems and Signal Processing, 93:379–396, 2017. doi:10.1016/j.ymssp.2016.12.023.

11

Charles Blundell, Julien Cornebise, Koray Kavukcuoglu, and Daan Wierstra. Weight uncertainty in neural networks. arXiv preprint arXiv:1505.05424, 2015.

12

Katalin Csilléry, Michael GB Blum, Oscar E Gaggiotti, and Olivier François. Approximate bayesian computation (abc) in practice. Trends in ecology & evolution, 25(7):410–418, 2010. doi:10.1016/j.tree.2010.04.001.

13

Jonathan Sadeghi, Marco de Angelis, and Edoardo Patelli. Frequentist history matching with interval predictor models. Applied Mathematical Modelling, 61:29–48, September 2018. doi:10.1016/j.apm.2018.04.003.

14

Samuel S Wilks. Determination of sample sizes for setting tolerance limits. The Annals of Mathematical Statistics, 12(1):91–96, 1941. doi:10.1214/aoms/1177731788.

15

Victoria Montgomery. New statistical metliods in risk assessment by probability bounds. PhD thesis, Durham University, 2009.

16

James O Berger. Statistical Decision Theory and Bayesian Analysis. Springer Science & Business Media, 1985. doi:10.1007/978-1-4757-4286-2.

17

Scott Ferson, Jason O’Rawe, and Michael Balch. Computing with confidence: imprecise posteriors and predictive distributions. In Vulnerability, Uncertainty, and Risks: Quantification, Mitigation, and Management, pages 895–904. 2014. doi:10.1061/9780784413609.091.

18

Andrey Kolmogoroff. Confidence limits for an unknown distribution function. The annals of mathematical statistics, 12(4):461–463, 1941. doi:10.1214/aoms/1177731684.

19

Scott Ferson, Vladik Kreinovich, Lev Ginzburg, Davis S Myers, and Kari Sentz. Constructing probability boxes and dempster-shafer structures. Technical Report, Technical report, Sandia National Laboratories, 2003.

20

NIST/SEMATECH. E-handbook of statistical methods. http://www.itl.nist.gov/div898/handbook, 2012.

21

Sheldon Ross. A first course in probability. Pearson, 2014.

22

C Sundararajan. Expert opinion in probabilistic structural mechanics. In Probabilistic Structural Mechanics Handbook, pages 261–279. Springer, 1995. doi:10.1007/978-1-4615-1771-9_12.

23

JE Oakley and A O’Hagan. SHELF: The Sheffield Elicitation Framework (Version 2.0). School of Mathematics and Statistics, University of Sheffield. 2010. URL: http://www.tonyohagan.co.uk/shelf/.

24

John Kruschke. Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press, 2014.

25

Scott Ferson, William L Oberkampf, and Lev Ginzburg. Validation of imprecise probability models. Int. J. Reliab. Saf, 3(1-3):3–22, 2009. doi:10.1504/IJRS.2009.026832.

26

Marco De Angelis. Efficient Random Set Uncertainty Quantification by means of Advanced Sampling Techniques. PhD thesis, University of Liverpool, 2015.

27

Diego A Alvarez. On the calculation of the bounds of probability of events using infinite random sets. International journal of approximate reasoning, 43(3):241–267, 2006. doi:10.1016/j.ijar.2006.04.005.

28

Edoardo Patelli, Diego A Alvarez, Matteo Broggi, and Marco de Angelis. Uncertainty management in multidisciplinary design of critical safety systems. Journal of Aerospace Information Systems, 12(1):140–169, 2014. doi:10.2514/1.I010273.

29

Matthias CM Troffaes. Imprecise Monte Carlo simulation and iterative importance sampling for the estimation of lower previsions. International Journal of Approximate Reasoning, 101:31–48, 2018. doi:10.1016/j.ijar.2018.06.009.

30

Roberto Rocchetta and Edoardo Patelli. Stochastic analysis and reliability-cost optimization of distributed generators and air source heat pumps. In System Reliability and Safety (ICSRS), 2017 2nd International Conference on, 31–35. IEEE, 2017. doi:10.1109/ICSRS.2017.8272792.

31

Andrei N. Kolmogorov. Foundations of the Theory of Probability. Chelsea Publishing Company, New York, 1950.

32

Jonathan Sadeghi, Marco De Angelis, and Edoardo Patelli. Analytic probabilistic safety analysis under severe uncertainty. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 6(1):04019019, 2020.

33

Reuven Y Rubinstein and Dirk P Kroese. Simulation and the Monte Carlo method. Volume 10. John Wiley & Sons, 2016.

34

William H Press, Brian P Flannery, Saul A Teukolsky, and William T Vetterling. Numeric recipes in c: the art of scientific computing. 1992.

35

Eric A Wan and Rudolph Van Der Merwe. The unscented kalman filter for nonlinear estimation. In Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No. 00EX373), 153–158. Ieee, 2000. doi:10.1109/ASSPCC.2000.882463.

36

Jeffrey K Uhlmann. Dynamic map building and localization: New theoretical foundations. PhD thesis, University of Oxford Oxford, 1995.

37

Han Zhang, Yabing Li, Jianjun Xiao, and Thomas Jordan. Preliminary study of condensation heat transfer uncertainty quantification using cfd code gasflow-mpi. In ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018). 2018.

38

G. Perret, S. Rahman, and D. Wicaksono. Deterministic sampling and gaussian process metamodel approach applied to a station black out accident model. In ANS Best Estimate Plus Uncertainty International Conference (BEPU 2018). 2018.

39

Ramon E. Moore, R. Baker Kearfott, and Michael J. Cloud. Introduction to interval analysis. Society for Industrial and Applied Mathematics, 2009. doi:10.1137/1.9780898717716.bm.

40

Vladik Kreinovich, Wolfram Luther, and Evgenija D. Popova. Special issue on “uncertainty modeling and analysis with intervals: foundations, tools, applications”. Soft Computing, 17(8):1315–1317, Aug 2013. doi:10.1007/s00500-013-1004-z.

41

Eldon R Hansen. A generalized interval arithmetic. In International Symposium on Interval Mathematics, 7–18. Springer, 1975. doi:10.1007/3-540-07170-9_2.

42

Kyoko Makino and Martin Berz. Taylor models and other validated functional inclusion methods. International Journal of Pure and Applied Mathematics, 6:239–316, 2003.

43

Nedialko S Nedialkov, Vladik Kreinovich, and Scott A Starks. Interval arithmetic, affine arithmetic, Taylor series methods: why, what next? Numerical Algorithms, 37(1-4):325–336, 2004. doi:10.1023/B:NUMA.0000049478.42605.cf.

44

Luis G Crespo, Daniel P Giesy, and Sean P Kenny. A unifying framework to uncertainty quantification of polynomial systems subject to aleatory and epistemic uncertainty. Reliable Computing, 17(2):97–127, 2012.

45

Stephen Boyd and Lieven Vandenberghe. Convex optimization. Cambridge University Press, 2004.

46

Sébastien Bubeck and others. Convex optimization: algorithms and complexity. Foundations and Trends® in Machine Learning, 8(3-4):231–357, 2015. doi:10.1561/2200000050.

47

V Kreinovich, J Beck, C Ferregut, A Sanchez, GR Keller, M Averill, and SA Starks. Monte-carlo-type techniques for processing interval uncertainty, and their engineering applications. In Proceedings of the workshop on reliable engineering computing, 15–17. 2004.

48

Yakov Ben-Haim and Isaac Elishakoff. Convex models of uncertainty in applied mechanics. Volume 25. Elsevier, 2013. doi:10.1137/1035076.

49

Jorge Stolfi and Luiz Henrique de Figueiredo. An introduction to affine arithmetic. Trends in Applied and Computational Mathematics, 4(3):297–312, 2003.

50

Bernard Chazelle. An optimal convex hull algorithm in any fixed dimension. Discrete & Computational Geometry, 10(4):377–409, Dec 1993. doi:10.1007/BF02573985.

51

Shiqi Wang, Yizheng Chen, Ahmed Abdou, and Suman Jana. Mixtrain: scalable training of formally robust neural networks. arXiv preprint arXiv:1811.02625, 2018.

52

Zhi-yue Huang and Bin-wu He. Volume of unit ball in an n-dimensional normed space and its asymptotic properties. Journal of Shanghai University (English Edition), 12(2):107–109, Apr 2008. doi:10.1007/s11741-008-0204-1.

53

David Meyer. Notes on maximization of inner products over norm balls. 2017. URL: http://www.1-4-5.net/~dmm/ml/sgn.pdf (visited on 2019-05-02).

54

Andrew Y Ng and Michael I Jordan. On discriminative vs. generative classifiers: a comparison of logistic regression and naive bayes. In Advances in neural information processing systems, 841–848. 2002.

55

Will Dabney, Mark Rowland, Marc G Bellemare, and Rémi Munos. Distributional reinforcement learning with quantile regression. The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18), 2017.

56

Márcio J Lacerda and Luis G Crespo. Interval predictor models for data with measurement uncertainty. In American Control Conference (ACC), 2017, 1487–1492. IEEE, 2017. doi:10.23919/ACC.2017.7963163.

57

Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep learning models resistant to adversarial attacks. ICML 2017 Workshop on Principled Approaches to Deep Learning, 2017.

58

Marco C Campi, Giuseppe Calafiore, and Simone Garatti. Interval predictor models: identification and reliability. Automatica, 45(2):382–392, 2009. doi:10.1016/j.automatica.2008.09.004.

59

Luis G Crespo, Sean P Kenny, and Daniel P Giesy. Interval predictor models with a linear parameter dependency. Journal of Verification, Validation and Uncertainty Quantification, 2016. doi:10.1115/1.4032070.

60

Hisao Ishibuchi, Hideo Tanaka, and Hidehiko Okada. An architecture of neural networks with interval weights and its application to fuzzy regression analysis. Fuzzy Sets and Systems, 57(1):27–39, 1993. doi:10.1016/0165-0114(93)90118-2.

61

Lei Huang, Bai-Ling Zhang, and Qian Huang. Robust interval regression analysis using neural networks. Fuzzy sets and systems, 97(3):337–347, 1998. doi:10.1016/S0165-0114(96)00325-9.

62

Steffen Freitag, Wolfgang Graf, and Michael Kaliske. Recurrent neural networks for fuzzy data. Integrated Computer-Aided Engineering, 18(3):265–280, 2011. doi:10.3233/ICA-2011-0373.

63

Raquel E Patiño-Escarcina, Benjamín R Callejas Bedregal, and Aarão Lyra. Interval computing in neural networks: one layer interval neural networks. In International Conference on Intelligent Information Technology, 68–75. Springer, 2004. doi:10.1007/978-3-540-30561-3_8.

64

Marco C Campi, Simone Garatti, and Federico A Ramponi. Non-convex scenario optimization with application to system identification. In 2015 54th IEEE Conference on Decision and Control (CDC), 4023–4028. IEEE, 2015. doi:10.1109/CDC.2015.7402845.

65

Algo Carè and Enrico Camporeale. Chapter 4 - regression. In Enrico Camporeale, Simon Wing, and Jay R. Johnson, editors, Machine Learning Techniques for Space Weather, pages 71 – 112. Elsevier, 2018. doi:10.1016/B978-0-12-811788-0.00004-4.

66

Jonathan Sadeghi, Marco De Angelis, and Edoardo Patelli. Efficient training of interval neural networks for imprecise training data. Neural Networks, 118:338–351, 2019.

67

Giuseppe Carlo Calafiore. Random convex programs. SIAM Journal on Optimization, 20(6):3427–3464, 2010. doi:10.1137/090773490.

68

Marco C Campi and Simone Garatti. The exact feasibility of randomized solutions of uncertain convex programs. SIAM Journal on Optimization, 19(3):1211–1230, 2008. doi:10.1137/07069821X.

69

Teodoro Alamo, Roberto Tempo, Amalia Luque, and Daniel R Ramirez. Randomized methods for design of uncertain systems: sample complexity and sequential algorithms. Automatica, 52:160–172, 2015. doi:10.1016/j.automatica.2014.11.004.

70

Javiera Barrera, Tito Homem-de-Mello, Eduardo Moreno, Bernardo K Pagnoncelli, and Gianpiero Canessa. Chance-constrained problems and rare events: an importance sampling approach. Mathematical Programming, 157(1):153–189, 2016. doi:10.1007/s10107-015-0942-x.

71

Algo Carè, Simone Garatti, and Marco C Campi. Scenario min-max optimization and the risk of empirical costs. SIAM Journal on Optimization, 25(4):2061–2080, 2015. doi:10.1137/130928546.

72

Marco C Campi and Simone Garatti. Wait-and-judge scenario optimization. Mathematical Programming, 167(1):155–189, 2018. doi:10.1007/s10107-016-1056-9.

73

Marco C Campi and Algo Caré. Random convex programs with l$_1$-regularization: sparsity and generalization. SIAM Journal on Control and Optimization, 51(5):3532–3557, 2013. doi:10.1137/110856204.

74

S. Garatti and M. C. Campi. Complexity-based modulation of the data-set in scenario optimization. In 2019 18th European Control Conference (ECC), volume, 1386–1391. June 2019. doi:10.23919/ECC.2019.8796160.

75

Marco Claudio Campi, Simone Garatti, and Federico Alessandro Ramponi. A general scenario theory for nonconvex optimization and decision making. IEEE Transactions on Automatic Control, 63(12):4067–4078, 2018. doi:10.1109/TAC.2018.2808446.

76

Edoardo Patelli, Matteo Broggi, Silvia Tolo, and Jonathan Sadeghi. Cossan software: a multidisciplinary and collaborative software for uncertainty quantification. In 2nd ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering, number UNCECOMP 2017. 2017. doi:10.7712/120217.5364.16982.

77

Jonathan Sadeghi. PyIPM. GitHub repository, 2018. URL: https://github.com/JCSadeghi/PyIPM, doi:10.5281/zenodo.3349670.

78

Sebastian Brandt, Matteo Broggi, Jan Hafele, Cristian Guillermo Gebhardt, Raimund Rolfes, and Michael Beer. Meta-models for fatigue damage estimation of offshore wind turbines jacket substructures. Procedia engineering, 199:1158–1163, 2017. doi:10.1016/j.proeng.2017.09.292.

79

Francisco Alejandro Diaz De la O. Gaussian process emulators for the analysis of complex models in engineering. PhD thesis, Swansea University, 2011.

80

Peter I Frazier. A tutorial on bayesian optimization. arXiv preprint arXiv:1807.02811, 2018.

81

Radford M Neal. Bayesian learning for neural networks. Volume 118. Springer Science & Business Media, 2012. doi:10.1007/978-1-4612-0745-0.

82

James Hensman, Nicolò Fusi, and Neil D Lawrence. Gaussian processes for big data. In Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence, 282–290. AUAI Press, 2013.

83

Marta Garnelo, Jonathan Schwarz, Dan Rosenbaum, Fabio Viola, Danilo J Rezende, SM Eslami, and Yee Whye Teh. Neural processes. arXiv preprint arXiv:1807.01622, 2018.

84

S. M. Ali Eslami, Danilo Jimenez Rezende, Frederic Besse, Fabio Viola, Ari S Morcos, Marta Garnelo, Avraham Ruderman, Andrei A Rusu, Ivo Danihelka, Karol Gregor, and others. Neural scene representation and rendering. Science, 360(6394):1204–1210, 2018. doi:10.1126/science.aar6170.

85

Roland Schöbi. Surrogate models for uncertainty quantification in the context of imprecise probability modelling. PhD thesis, ETH Zurich, 2017.

86

C Raj Sundararajan. Probabilistic structural mechanics handbook: theory and industrial applications. Springer Science & Business Media, 2012. doi:10.1007/978-1-4615-1771-9.

87

Yarin Gal. Uncertainty in deep learning. PhD thesis, PhD thesis, University of Cambridge, 2016.

88

Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems, 2672–2680. 2014.

89

Carl Doersch. Tutorial on variational autoencoders. arXiv preprint arXiv:1606.05908, 2016.

90

Sebastian Ruder. An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747, 2016.

91

Diederik P Kingma and Jimmy Ba. Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.

92

Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, and Ruslan Salakhutdinov. Dropout: a simple way to prevent neural networks from overfitting. The Journal of Machine Learning Research, 15(1):1929–1958, 2014.

93

Yarin Gal and Zoubin Ghahramani. Dropout as a bayesian approximation: representing model uncertainty in deep learning. In international conference on machine learning, 1050–1059. 2016.

94

Yarin Gal, Jiri Hron, and Alex Kendall. Concrete dropout. In Advances in Neural Information Processing Systems, 3581–3590. 2017.

95

Yarin Gal. Heteroscedastic dropout uncertainty. https://github.com/yaringal/HeteroscedasticDropoutUncertainty, 2016.

96

V. N. Vapnik and A. Ya. Chervonenkis. On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities, pages 11–30. Springer International Publishing, Cham, 2015. doi:10.1007/978-3-319-21852-6_3.

97

Isaac Elishakoff and Makoto Ohsaki. Optimization and anti-optimization of structures under uncertainty. World Scientific, 2010. doi:10.1142/p678.

98

Yakov Ben-Haim. Convex models of uncertainty: applications and implications. Erkenntnis, 41(2):139–156, 1994. doi:10.1007/BF01128824.

99

Diego A Alvarez. Infinite random sets and applications in uncertainty analysis. PhD thesis, Ph. D. Thesis, Leopold-Franzens Universität Innsbruck, Innsbruck, Austria, 2007.

100

Thomas Fetz and Michael Oberguggenberger. Imprecise random variables, random sets, and monte carlo simulation. International Journal of Approximate Reasoning, 78:252–264, 2016. doi:10.1016/j.ijar.2016.06.012.

101

Zhiping Qiu, Di Yang, and Isaac Elishakoff. Probabilistic interval reliability of structural systems. International Journal of Solids and Structures, 45(10):2850–2860, 2008. doi:10.1016/j.ijsolstr.2008.01.005.

102

C Jiang, J Zheng, and X Han. Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: a review. Structural and Multidisciplinary Optimization, pages 1–18, 2017. doi:10.1007/s00158-017-1864-4.

103

Arne Decadt, Gert de Cooman, and Jasper De Bock. Monte carlo estimation for imprecise probabilities: basic properties. arXiv preprint arXiv:1905.09301, 2019.

104

Roland Schöbi and Bruno Sudret. Structural reliability analysis for p-boxes using multi-level meta-models. Probabilistic Engineering Mechanics, 48:27–38, 2017. doi:10.1016/j.probengmech.2017.04.001.

105

Jonathan Sadeghi, Marco de Angelis, and Edoardo Patelli. Robust propagation of probability boxes by interval predictor models. Structural Safety, 82:101889, 2020.

106

Robert E Melchers and André T Beck. Structural reliability analysis and prediction. John Wiley & Sons, 2018.

107

Nawal K. Prinja, Azeezat Ogunbadejo, Jonathan Sadeghi, and Edoardo Patelli. Structural reliability of pre-stressed concrete containments. Nuclear Engineering and Design, December 2016. doi:10.1016/j.nucengdes.2016.11.036.

108

Zygmund William Birnbaum. On the importance of different components in a multicomponent system. Technical Report, Washington Univ Seattle Lab of Statistical Research, 1968.

109

Andrea Saltelli, Stefano Tarantola, Francesca Campolongo, and Marco Ratto. Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. John Wiley & Sons, 2004. doi:10.1002/0470870958.

110

Edoardo Patelli, Helmut J Pradlwarter, and Gerhart I Schuëller. Global sensitivity of structural variability by random sampling. Computer Physics Communications, 181(12):2072–2081, 2010. doi:10.1016/j.cpc.2010.08.007.

111

Stefano Tarantola, Debora Gatelli, and Thierry Alex Mara. Random balance designs for the estimation of first order global sensitivity indices. Reliability Engineering & System Safety, 91(6):717–727, 2006. doi:10.1016/j.ress.2005.06.003.

112

Ronald L. Iman. Latin Hypercube Sampling. New York: John Wiley & Sons Ltd, 2014. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118445112.stat03803, doi:10.1002/9781118445112.stat03803.

113

Karl Breitung. Asymptotic approximations for multinormal integrals. Journal of Engineering Mechanics, 110(3):357–366, 1984.

114

K.W. Breitung. Asymptotic Approximations for Probability Integrals. Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1994. ISBN 9783540586173. URL: https://books.google.co.uk/books?id=f9AZAQAAIAAJ.

115

Karl Breitung. 40 years form: some new aspects? Probabilistic Engineering Mechanics, 42:71–77, 2015. URL: https://www.sciencedirect.com/science/article/pii/S0266892015300369, doi:https://doi.org/10.1016/j.probengmech.2015.09.012.

116

Marco de Angelis, Edoardo Patelli, and Michael Beer. Advanced line sampling for efficient robust reliability analysis. Structural safety, 52:170–182, 2015. doi:10.1016/j.strusafe.2014.10.002.

117

Gerhart Iwo Schuëller and Reinhard Stix. A critical appraisal of methods to determine failure probabilities. Structural Safety, 4(4):293–309, 1987. doi:10.1016/0167-4730(87)90004-X.

118

Siu-Kui Au and James L Beck. Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic engineering mechanics, 16(4):263–277, 2001. doi:10.1016/S0266-8920(01)00019-4.

119

Karl Breitung. The geometry of limit state function graphs and subset simulation: counterexamples. Reliability Engineering & System Safety, 182:98–106, 2019. doi:10.1016/j.ress.2018.10.008.

120

Christian G Bucher and U Bourgund. A fast and efficient response surface approach for structural reliability problems. Structural safety, 7(1):57–66, 1990. doi:10.1016/0167-4730(90)90012-E.

121

Claudio M Rocco and José Alı́ Moreno. Fast monte carlo reliability evaluation using support vector machine. Reliability Engineering & System Safety, 76(3):237–243, 2002. doi:10.1016/S0951-8320(02)00015-7.

122

Marc Berveiller, Bruno Sudret, and Maurice Lemaire. Stochastic finite element: a non intrusive approach by regression. European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique, 15(1-3):81–92, 2006. doi:10.3166/remn.15.81-92.

123

Shaowen Shao and Yoshisada Murotsu. Structural reliability analysis using a neural network. JSME International Journal Series A Solid Mechanics and Material Engineering, 40(3):242–246, 1997. doi:10.1299/jsmea.40.242.

124

Irfan Kaymaz. Application of kriging method to structural reliability problems. Structural Safety, 27(2):133–151, 2005. doi:10.1016/j.strusafe.2004.09.001.

125

Bruno Sudret. Global sensitivity analysis using polynomial chaos expansions. Reliability engineering & system safety, 93(7):964–979, 2008. doi:10.1016/j.ress.2007.04.002.

126

Matthias Faes, Jonathan Sadeghi, Matteo Broggi, Marco De Angelis, Edoardo Patelli, Michael Beer, and David Moens. On the robust estimation of small failure probabilities for strong non-linear models. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems Part B: Mechanical Engineering, 2019. URL: https://www.researchgate.net/publication/330765220_On_the_robust_estimation_of_small_failure_probabilities_for_strong_non-linear_models.

127

Bruno Sudret. Meta-models for structural reliability and uncertainty quantification. In “Asian-Pacific Symposium on Structural Reliability and its Applications”, 1–24. 2012.

128

B Echard, N Gayton, and M Lemaire. Ak-mcs: an active learning reliability method combining kriging and monte carlo simulation. Structural Safety, 33(2):145–154, 2011. doi:10.1016/j.strusafe.2011.01.002.

129

Barry J Goodno and James M Gere. Mechanics of Materials. Cengage Learning, 2016.

130

Edoardo Patelli, Silvia Tolo, Hindolo George-Williams, Jonathan Sadeghi, Roberto Rocchetta, Marco de Angelis, and Matteo Broggi. Opencossan 2.0: an efficient computational toolbox for risk, reliability and resilience analysis. In Proceedings of the joint ASCE ICVRAM ISUMA UNCERTAINTIES conference. 2018. URL: http://icvramisuma2018.org/cd/web/PDF/ICVRAMISUMA2018-0022.PDF.

131

Jonathan Sadeghi. Uncertainty Modelling for Scarce and Imprecise Data in Engineering Applications. PhD thesis, University of Liverpool, 2020. doi:10.17638/03089368.

132

Wellison JS Gomes. Structural reliability analysis using adaptive artificial neural networks. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 2019. doi:10.1115/1.4044040.

133

US Nuclear Regulatory Commission. Guidance on the treatment of uncertainties associated with pras in risk-informed decision making. NUREG-1855, March 2009.

134

US Nuclear Regulatory Commission. Probabilistic risk assessment and regulatory decision making: some frequently asked questions. NUREG-2201, September 2016.

135

James Berger. The robust Bayesian viewpoint (with discussion). Robustness of Bayesian Analysis. Amsterdam: North Holland, 1984.

136

James O Berger, Elías Moreno, Luis Raul Pericchi, M Jesús Bayarri, José M Bernardo, Juan A Cano, Julián De la Horra, Jacinto Martín, David Ríos-Insúa, Bruno Betrò, and others. An overview of robust Bayesian analysis. Test, 3(1):5–124, 1994. doi:10.1007/BF02562676.

Conclusion