Concept
Théorie des possibilités
Concepts associés (4)
Upper and lower probabilities
Upper and lower probabilities are representations of imprecise probability. Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur, this method uses two numbers: the upper probability of the event and the lower probability of the event. Because frequentist statistics disallows metaprobabilities, frequentists have had to propose new solutions. Cedric Smith and Arthur Dempster each developed a theory of upper and lower probabilities.
Imprecise probability
Imprecise probability generalizes probability theory to allow for partial probability specifications, and is applicable when information is scarce, vague, or conflicting, in which case a unique probability distribution may be hard to identify. Thereby, the theory aims to represent the available knowledge more accurately. Imprecision is useful for dealing with expert elicitation, because: People have a limited ability to determine their own subjective probabilities and might find that they can only provide an interval.
Logique probabiliste
Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logic truth tables with probabilistic expressions. A difficulty of probabilistic logics is their tendency to multiply the computational complexities of their probabilistic and logical components. Other difficulties include the possibility of counter-intuitive results, such as in case of belief fusion in Dempster–Shafer theory.
Espace probabilisé
Un espace de probabilité(s) ou espace probabilisé est construit à partir d'un espace probabilisable en le complétant par une mesure de probabilité : il permet la modélisation quantitative de l'expérience aléatoire étudiée en associant une probabilité numérique à tout événement lié à l'expérience. Formellement, c'est un triplet formé d'un ensemble , d'une tribu sur et d'une mesure sur cette tribu tel que . L'ensemble est appelé l'univers et les éléments de sont appelés les événements.