On the quantification and efficient propagation of imprecise probabilities resulting from small datasets

Der Kiureghian, 2009, Aleatory or epistemic? Does it matter?, Struct. Saf., 31, 105, 10.1016/j.strusafe.2008.06.020 Ferson, 1996, Different methods are needed to propagate ignorance and variability, Reliab. Eng. Syst. Saf., 54, 133, 10.1016/S0951-8320(96)00071-3 Dempster, 1967, Upper and lower probabilities induced by a multivalued mapping, Ann. Math. Stat., 325, 10.1214/aoms/1177698950 Shafer, 1976, vol. 1 Zadeh, 1965, Fuzzy sets, Inf. Control, 8, 338, 10.1016/S0019-9958(65)90241-X Moore, 1979, vol. 2 Weichselberger, 2000, The theory of interval-probability as a unifying concept for uncertainty, Int. J. Approx. Reason., 24, 149, 10.1016/S0888-613X(00)00032-3 Ben-Haim, 2013, vol. 25 Dubois, 2012 Klir, 2005 Molchanov, 2005, vol. 53 Ferson, 2002 Ferson, 2004, Arithmetic with uncertain numbers: rigorous and (often) best possible answers, Reliab. Eng. Syst. Saf., 85, 135, 10.1016/j.ress.2004.03.008 Raftery, 1995, Bayesian model selection in social research, Sociol. Methodol., 111, 10.2307/271063 Pawitan, 2001 Dubois, 1991, Random sets and fuzzy interval analysis, Fuzzy Sets Syst., 42, 87, 10.1016/0165-0114(91)90091-4 D. Dubois, H. Prade, Interval-valued fuzzy sets, possibility theory and imprecise probability, in: EUSFLAT Conf., 2005, pp. 314–319. Fetz, 2004, Propagation of uncertainty through multivariate functions in the framework of sets of probability measures, Reliab. Eng. Syst. Saf., 85, 73, 10.1016/j.ress.2004.03.004 Walley, 1991, vol. 42 Walley, 2000, Towards a unified theory of imprecise probability, Int. J. Approx. Reason., 24, 125, 10.1016/S0888-613X(00)00031-1 Beer, 2013, Imprecise probabilities in engineering analyses, Mech. Syst. Signal Process., 37, 4, 10.1016/j.ymssp.2013.01.024 Der Kiureghian, 1989, Measures of structural safety under imperfect states of knowledge, J. Struct. Eng., 115, 1119, 10.1061/(ASCE)0733-9445(1989)115:5(1119) Zhang, 2001, Integration of computation and testing for reliability estimation, Reliab. Eng. Syst. Saf., 74, 13, 10.1016/S0951-8320(01)00008-4 Der Kiureghian, 2008, Analysis of structural reliability under parameter uncertainties, Probab. Eng. Mech., 23, 351, 10.1016/j.probengmech.2007.10.011 Halpern, 2000, Representing both first-and second-order uncertainties by Monte Carlo simulation for groups of patients, Med. Decis. Making, 20, 314, 10.1177/0272989X0002000308 Hoeting, 1999, Bayesian model averaging: a tutorial, Stat. Sci., 382 Massey, 1951, The Kolmogorov-Smirnov test for goodness of fit, J. Am. Stat. Assoc., 46, 68, 10.1080/01621459.1951.10500769 Bernardo, 2002, Bayesian hypothesis testing: a reference approach, Int. Stat. Rev., 70, 351, 10.1111/j.1751-5823.2002.tb00175.x Akaike, 1974, A new look at the statistical model identification, IEEE Trans. Autom. Control, 19, 716, 10.1109/TAC.1974.1100705 Browne, 1993, Alternative ways of assessing model fit, Sage Focus Ed., 154, 136 Sankararaman, 2013, Distribution type uncertainty due to sparse and imprecise data, Mech. Syst. Signal Process., 37, 182, 10.1016/j.ymssp.2012.07.008 Burnham, 2004, Multimodel inference understanding AIC and BIC in model selection, Sociol. Meth. Res., 33, 261, 10.1177/0049124104268644 Efron, 1979, Bootstrap methods: another look at the jackknife, Ann. Stat., 7, 1, 10.1214/aos/1176344552 Sankararaman, 2011, Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data, Reliab. Eng. Syst. Saf., 96, 814, 10.1016/j.ress.2011.02.003 Goodman, 2010, Ensemble samplers with affine invariance, Commun. Appl. Math. Comput. Sci., 5, 65, 10.2140/camcos.2010.5.65 Foreman-Mackey, 2013, emcee: The MCMC hammer, Publ. Astron. Soc. Pac., 125, 306, 10.1086/670067 Kullback, 1951, On information and sufficiency, Ann. Math. Stat., 22, 79, 10.1214/aoms/1177729694 Weakliem, 1999, A critique of the Bayesian information criterion for model selection, Sociol. Meth. Res., 27, 359, 10.1177/0049124199027003002 Hurvich, 1989, Regression and time series model selection in small samples, Biometrika, 76, 297, 10.1093/biomet/76.2.297 Hurvich, 1995, Model selection for extended quasi-likelihood models in small samples, Biometrics, 1077, 10.2307/2533006 Csisz, 1963, Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten, Publ. Math. Inst. Hungar. Acad., 8, 95 Morimoto, 1963, Markov processes and the h-theorem, J. Phys. Soc. Jpn., 18, 328, 10.1143/JPSJ.18.328 Ali, 1966, A general class of coefficients of divergence of one distribution from another, J. Roy. Stat. Soc. Ser. B (Meth.), 131 Hellinger, 1909, Neue Begründung der Theorie quadratischer Formen von unendlich vielen Veränderlichen, Journal für die Reine und Angewandte Mathematik, 136, 210, 10.1515/crll.1909.136.210 Gibbs, 2002, On choosing and bounding probability metrics, Int. Stat. Rev., 70, 419, 10.1111/j.1751-5823.2002.tb00178.x Beran, 1977, Minimum Hellinger distance estimates for parametric models, Ann. Stat., 445 Lindsay, 1994, Efficiency versus robustness: the case for minimum Hellinger distance and related methods, Ann. Stat., 1081 Owen, 2000, Safe and effective importance sampling, J. Am. Stat. Assoc., 95, 135, 10.1080/01621459.2000.10473909 D. Faulkner, A review of effective plating to be used in the analysis of stiffened plating in bending and compression, Tech. rep., 1973. Carlsen, 1977, Simplified collapse analysis of stiffened plates, Norw. Maritime Res., 5 Hess, 2002, Uncertainties in material and geometric strength and load variables, Naval Eng. J., 114, 139, 10.1111/j.1559-3584.2002.tb00128.x Soares, 1988, Uncertainty modelling in plate buckling, Struct. Saf., 5, 17, 10.1016/0167-4730(88)90003-3 Saltelli, 2008 Cannavó, 2012, Sensitivity analysis for volcanic source modeling quality assessment and model selection, Comput. Geosci., 44, 52, 10.1016/j.cageo.2012.03.008 Sobol, 2001, Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simul., 55, 271, 10.1016/S0378-4754(00)00270-6 Saltelli, 1998, An alternative way to compute fourier amplitude sensitivity test (fast), Comput. Stat. Data Anal., 26, 445, 10.1016/S0167-9473(97)00043-1