theory.md

Theory

TODO

However Probability bounds analysis and probability boxes are comprehensive

Bibliography

For probability bound analysis:

• Ferson, S., V. Kreinovich, L. Ginzburg, K. Sentz and D.S. Myers. 2003. Constructing probability boxes and Dempster-Shafer structures. Sandia National Laboratories, SAND2002-4015, Albuquerque, New Mexico
• Ferson, S., and J. Siegrist. 2012. Verified computation with probabilities. Pages 95-122 in Uncertainty Quantification in Scientific Computing, edited by A. Dienstfrey and R.F. Boisvert, Springer, New York
• Beer, M., S. Ferson, and V. Kreinovich. 2013. Imprecise probabilities in engineering analyses. Mechanical Systems and Signal Processing 37: 429
• Ferson, S., D.R.J. Moore, P. van der Brink, T.L. Estes, K. Gallagher, R. O’Connor and F. Verdonck. 2010. Bounding uncertainty analyses. Application of Uncertainty Analysis to Ecological Risks of Pesticides

For interval statistics:

• Ferson, Scott, et al. "Experimental uncertainty estimation and statistics for data having interval uncertainty." Sandia National Laboratories, Report SAND2007-0939 162 (2007)

For dependency modelling:

• Ferson, S., R. Nelsen, J. Hajagos, D. Berleant, J. Zhang, W.T. Tucker, L. Ginzburg and W.L. Oberkampf. 2004. Dependence in Probabilistic Modeling, Dempster-Shafer Theory, and Probability Bounds Analysis. Sandia National Laboratories, SAND2004-3072, Albuquerque, NM

• Nelsen, Roger B. An introduction to copulas. Springer Science & Business Media, 2007