The central idea of this course is that probability descriptions are mathematical models that should faithfully represent the degree of precision inherent in the background knowledge about the empirical domain being modeled. The very high precision of the real numbers may greatly exceed the modeler's understanding of, and available data about, the random, chance, indeterminate, non-deterministic, vague, fuzzy or imprecise empirical domain (e.g., guilt of an individual in a court, medical diagnosis of a specific patient, immediate winter driving conditions, global climate forecast) being modeled. Hence, we need a spectrum of mathematical representations to complement the present-day, nearly universally agreed upon, use of the unit interval [0,1] to represent additive probabilities.
We will explore multiple meanings (interpretations) and axiomatizations of probability and some of the connections to probabilistic reasoning (e.g., inference, decisions). Meanings include: common subsymbolic usage; ordinary language usage; degree of belief held by an individual; epistemic or partial logical linkage between statements or data sets; stable and unstable frequentist understandings of repeatable phenomena; and prosensities. The emphasis will be on mathematical probability concepts that are either not real-valued (e.g., modal, comparative, interval-valued, sets of measures-valued or, if real-valued, that depart from the usual axiomatic structure (e.g., semicomputable semimeasures).
| CRN | Course | Course Title | Term | Credits | Status | ||||
| 89300 | CSC 577 | MATH. ALT. TO STANDARD PROB. | Spring 2013 | 4.0 | Open | ||||
| Schedule: | Day | Begin | End | Building | Room | ||||
| T | 1400 | 1515 | CSB | 632 | |||||
| Enrollment: | Sec Enroll | Sec Cap | Updated | ||||||
| 0 | 999 | 12/13/2012 | |||||||