Série de cours "Imprecise Probability", Inès Couso, Université d'Oviedo

9 - 21 Jan. 2015

Dans le cadre de son invitation par le LabEx CIMI en tant qu'expert scientifique pour une durée de trois mois en 2015, la professeur Inès Couso de l'université d'Oviedo, donnera une série de cours intitulée "Imprecise Probabilities" pendant le mois de janvier 2015  .

 

Lieu :

 

Auditorium J. Herbrandt, IRIT, rez de chaussée
 
 

Cours 1: Precise probabilities and motivation for imprecise probabilities (2 heures)

Vendredi 9 janvier, 10h-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

Cours 2: Mathematical models in Imprecise Probabilities (4 heures)

Lundi 12 janvier, 10h-12h et Mercredi 14 janvier, 10h-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

 
Cours 3: Epistemic random sets (4 heures)

Vendredi 16 janvier, 10h-12h et Lundi 19 janvier 10h-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

 
Cours 4: Generalized stochastic orderings (2 heures)

Mercredi 21 janvier, 10h-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.
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