Imprecise Probability Course by Inès Couso, University of Oviedo
9 - 21 Jan. 2015
As part of her invitation by CIMI as an Excellence Advanced Researcher for three months in 2015, Inès Couso from the University of Oviedo, will give a series of courses in January on Imprecise Probabilities.
Auditorium J. Herbrandt, IRIT, ground floor.
Course 1: Precise probabilities and motivation for imprecise probabilities (2 hours)
Friday January 9th, 10-12h
- Frequentist approach to probability theory. Kolmogorov axioms.
- Subjective approach to probability theory. Betting prices.
- Shortcomings of probability theory: illustrative examples.
- Simple representations using some particular imprecise probabilities models:
- Possibility and necessity measures: well known inequalities in Statistics (Chebycheff, etc). Nested confidence intervals.
- Plausibility and belief measures: upper and lower probabilities induced by multi-valued mappings
Course 2: Mathematical models in Imprecise Probabilities (4 hours)
Monday January 12th, 10-12h and Wednesday January 14th, 10-12h
- possibility and necessity measures. Nested focal sets.
- plausibility and belief measures
- second-order Choquet capacities
- coherent upper and lower probabilities
- coherent upper and lower previsions
- sets of probability measures
- sets of desirable gambles
- partial preference orderings
Course 3: Epistemic random sets (4 hours)
Friday January 16th, 10-12h and Monday January 19th, 10-12h
- Conjunctive vs Disjunctive sets
- Mathematical foundations of random sets
- Basic mass assignments
- Epistemic interpretation of random sets
- Belief and plausibility functions
- Statistics with interval data
- Consonant random sets and possibility measures
Course 4: Generalized stochastic orderings (2 hours)
Wednesday January 21st, 10-12h
- Stochastic orderings: expected utility, statistical preference, first stochastic dominance.
- Generalized forms of stochastic orderings: combinations of interval comparisons and stochastic orderings.
- Relation between Walley's preference orderings and generalized stochastic orderings.