Mathematical foundations for a theory of confidence structures

Fisher, 1957 Mayo, 1996 M.S. Balch, Ph.D. Dissertation: Methods for Rigorous Uncertainty Quantification with Application to a Mars Atmosphere Model, Virginia Tech, Blacksburg, VA, 2010. Barnett, 1999 Cox, 2006 Schweder, 2002, Confidence and Likelihood, Scandinavian Journal of Statistics, 29, 309, 10.1111/1467-9469.00285 Singh, 2007, Confidence Distribution (CD): Distribution Estimator of a Parameter, Lecture Notes-Monograph Series, 54, 132, 10.1214/074921707000000102 Dempster, 2008, A generalization of Bayesian inference, 73 Shafer, 2008, Allocations of probability, 183 Dempster, 2008, The Dempster–Shafer calculus for statisticians, International Journal of Approximate Reasoning, 48, 365, 10.1016/j.ijar.2007.03.004 Casella, 2002 Kyburg, 1974 Molchanov, 2005 Yager, 2008, Classic works of the dempster shafer theory of belief functions: an introduction, 1 Salicone, 2007 Zadeh, 1965, Fuzzy sets, Information and Control, 8, 338, 10.1016/S0019-9958(65)90241-X Dubois, 2008, A set-theoretic view of belief functions: logical operations and approximations by fuzzy sets, 375 Fisher, 1935, The fiducial argument in statistical inference, Annals of Eugenics, 6, 391, 10.1111/j.1469-1809.1935.tb02120.x Williamson, 1990, Probabilistic arithmetic. I. Numerical methods for calculating convolutions and dependency bounds, International Journal of Approximate Reasoning, 4, 89, 10.1016/0888-613X(90)90022-T Joslyn, 2005, Approximate representations of random intervals for hybrid uncertainty quantification in engineering modeling Efron, 1998, R.A. Fisher in the 21st Century, Statistical Science, 13, 95 Savage, 1972 Kohlas, 1995 Fraser, 1966, Structural Probability and a Generalization, Biometrika, 53, 1, 10.1093/biomet/53.1-2.1 Dempster, 2008, Logicist statistics II: inference, 761 Dempster, 2008, New methods for reasoning towards posterior distributions based on sample data, 35 Zhang, 2011, Dempster–Shafer inference with weak beliefs, Statistica Sinica, 21, 475, 10.5705/ss.2011.022a Walley, 2002, Reconciling frequentist properties with the likelihood principle, Journal of Statistical Planning and Inference, 105, 35, 10.1016/S0378-3758(01)00203-8