Random Sets and Exact Confidence Regions

Aregui, A. and Denœux, T. (2008). Constructing consonant belief functions from sample data using confidence sets of pignistic probabilities. Internat. J. Approx. Reason., 49, 575–594.

Balch, M.S. (2012). Mathematical foundations for a theory of confidence structures. Internat. J. Approx. Reason., 53, 1003–1019.

Crow, H.L. (1974). Reliability analysis for complex, repairable systems. In Reliability and Biometry (F. Proschan and R.J. Serfling, eds.). Society for Industrial and Applied Mathematics (SIAM), Philadelphia, pp. 379–410.

Dempster, A.P. (1967). Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Statist., 38, 325–339.

Dempster, A.P. (2008). Dempster–Shafer calculus for statisticians. Internat. J. Approx. Reason., 48, 265–277.

Efron, B. and Tibshirani, R.J. (1993). An introduction to the bootstrap. Chapman and Hall, New York.

Ermini Leaf, D. and Liu, C. (2012). Inference about constrained parameters using the elastic belief method. Internat. J. Approx. Reason., 53, 709–727.

Gaudoin, O., Yang, B., and Xie, M. (2006). Confidence intervals for the scale parameter of the power-law process. Comm. Statist. Theory Methods, 35, 1525–1538.

Martin, R. and Liu, C. (2013a). Conditional inferential models: combining information for prior-free probabilistic inference. arXiv: 1211.1530 .

Martin, R. and Liu, C. (2013b). Correction: ‘Inferential models: A framework for prior-free posterior-posterior probabilistic inference’. J. Amer. Statist. Assoc., 108, 1138–1139.

Martin, R. and Liu, C. (2013c). Inferential models: A framework for prior-free posterior probabilistic inference. J. Amer. Statist. Assoc., 108, 301–313.

Martin, R. and Liu, C. (2013d). Marginal inferential models: prior-free probabilistic inference on interest parameters. arXiv: 1306.3092 .

Martin, R., Zhang, J., and Liu, C. (2010). Dempster–Shafer theory and statistical inference with weak beliefs. Statist. Sci., 25, 72–87.

Molchanov, I. (2005). Theory of random sets. Probability and its Applications (New York). Springer-Verlag London Ltd., London.

Nguyen, H.T. (1978). On random sets and belief functions. J. Math. Anal. Appl., 65, 531–542.

Shafer, G. (1976). A mathematical theory of evidence. Princeton University Press, Princeton, N.J.

Shafer, G. (1979). Allocations of probability. Ann. Probab., 7, 827–839.

Shafer, G. (1987). Belief functions and possibility measures. In The analysis of fuzzy information, Vol. 1: mathematics and logic (J.C. Bezdek, ed.). CRC, pp. 51–84.

Yager, R. and Liu, L. eds. (2008). Classic works of the Dempster–S hafer theory of belief functions, 219. Springer, Berlin.

Zhang, J. and Liu, C. (2011). Dempster–Shafer inference with weak beliefs. Statist. Sinica, 21, 475–494.