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.

Location :


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.