Statistical Modeling with Imprecise Probabilities
Abstract
The objective of this project is to develop theoretical foundations, based upon the broad framework of the theory of fuzzy measures, and methodology, supported by appropriate computer software, for systems modeling with imprecise probabilities of various kinds. This objective is motivated by the recognition that the assumption that relevant probabilities can be assessed precisely is highly unrealistic. The results are loosely classified into the following seven areas: (1) Complete methodology for Bayesian inference based upon interval valued or fuzzy probabilities and likelihoods; (2) Well justified information measure in Dempster Shafer theory; (3) Relevant theoretical results in fuzzy measure theory, a theory that is connected with imprecise probabilities in a similar way as classical measure theory is connected with classical probabilities; (4) Procedures for constructing imprecise probabilities and fuzzy measures by various methods, including the use of neural networks and genetic algorithms; (5) Various other theoretical results that emerged from the work on the project, including (a) Complete representations of Dempster Shafer theory and possibility theory in terms of the usual semantics of propositional modal logic, (b) Basic ideas of mathematics of finite resolution, (c) Constrained fuzzy arithmetic, (d) A method for identifying key variables in systems modeling via fuzzy c-means clustering based on varying distance function, and (e) A thorough mathematical analysis of the well known Cox's proof, by which it is shown that the proof does not demonstrate the inevitability of the rules of classical Bayesian inference, as often claimed; (6) Applications of the Bayesian inference with fuzzy probabilities to the problem of military unit identification and to statistical decision making; and (7) Computer programs for some algorithms that emerged from the work on this project.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1998
- Accession Number
- ADA354584
Entities
People
- George J. Klir
Organizations
- Binghamton University