Documents

44 pages

Obtenez un accès à la bibliothèque pour le consulter en ligne

__
En savoir plus
__

Description

Niveau: Secondaire, Lycée

A survey of the theory of coherent lower previsions Enrique Miranda? Abstract This paper presents a summary of Peter Walley's theory of coherent lower pre- visions. We introduce three representations of coherent assessments: coherent lower and upper previsions, closed and convex sets of linear previsions, and sets of desirable gambles. We show also how the notion of coherence can be used to update our beliefs with new information, and a number of possibilities to model the notion of independence with coherent lower previsions. Next, we comment on the connection with other approaches in the literature: de Finetti's and Williams' earlier work, Kuznetsov's and Weischelberger's work on interval-valued probabil- ities, Dempster-Shafer theory of evidence and Shafer and Vovk's game-theoretic approach. Finally, we present a brief survey of some applications and summarize the main strengths and challenges of the theory. Keywords. Subjective probability, imprecision, avoiding sure loss, coherence, desir- ability, conditional lower previsions, independence. 1 Introduction This paper aims at presenting the main facts about the theory of coherent lower previ- sions. This theory falls within the subjective approach to probability, where the prob- ability of an event represents our information about how likely is this event to happen. This interpretation of probability is mostly used in the framework of decision making, and is sometimes referred to as epistemic probability [30, 43].

A survey of the theory of coherent lower previsions Enrique Miranda? Abstract This paper presents a summary of Peter Walley's theory of coherent lower pre- visions. We introduce three representations of coherent assessments: coherent lower and upper previsions, closed and convex sets of linear previsions, and sets of desirable gambles. We show also how the notion of coherence can be used to update our beliefs with new information, and a number of possibilities to model the notion of independence with coherent lower previsions. Next, we comment on the connection with other approaches in the literature: de Finetti's and Williams' earlier work, Kuznetsov's and Weischelberger's work on interval-valued probabil- ities, Dempster-Shafer theory of evidence and Shafer and Vovk's game-theoretic approach. Finally, we present a brief survey of some applications and summarize the main strengths and challenges of the theory. Keywords. Subjective probability, imprecision, avoiding sure loss, coherence, desir- ability, conditional lower previsions, independence. 1 Introduction This paper aims at presenting the main facts about the theory of coherent lower previ- sions. This theory falls within the subjective approach to probability, where the prob- ability of an event represents our information about how likely is this event to happen. This interpretation of probability is mostly used in the framework of decision making, and is sometimes referred to as epistemic probability [30, 43].

- can also
- should agree
- previsions
- gambles
- probabilities when
- probability
- main facts
- his supremum acceptable
- vovk's recent

Sujets

Informations

Publié par | sucun |

Nombre de visites sur la page | 31 |

Langue | English |

Signaler un problème