Updating coherent previsions on finite spaces

Authors:
Enrique Miranda
Affiliations:
Department of Statistics and Operations Research, University of Oviedo, C-Calvo Sotelo, s/n 33007 Oviedo, Spain
Venue:
Fuzzy Sets and Systems
Year:
2009

Citing 10
Cited 13

Measures of uncertainty in expert systems

Artificial Intelligence
Bayesian conditioning in possibility theory

Fuzzy Sets and Systems - Special issue on fuzzy measures and integrals
Fuzzy sets as a basis for a theory of possibility

Fuzzy Sets and Systems
Credal networks

Artificial Intelligence
A new approach to updating beliefs

UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Updating beliefs with incomplete observations

Artificial Intelligence
Notes on conditional previsions

International Journal of Approximate Reasoning
A survey of the theory of coherent lower previsions

International Journal of Approximate Reasoning
Coherence graphs

Artificial Intelligence
The inferential complexity of Bayesian and credal networks

IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence

Conservative inference rule for uncertain reasoning under incompleteness

Journal of Artificial Intelligence Research
Correction of incoherent conditional probability assessments

International Journal of Approximate Reasoning
Independent natural extension

IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
An aggregation framework based on coherent lower previsions: Application to Zadeh's paradox and sensor networks

International Journal of Approximate Reasoning
Epistemic irrelevance in credal nets: The case of imprecise Markov trees

International Journal of Approximate Reasoning
Independent natural extension

Artificial Intelligence
A logical characterization of coherence for imprecise probabilities

International Journal of Approximate Reasoning
Notes on desirability and conditional lower previsions

Annals of Mathematics and Artificial Intelligence
Imprecise probabilities for representing ignorance about a parameter

International Journal of Approximate Reasoning
Incoherence correction strategies in statistical matching

International Journal of Approximate Reasoning
Probability and time

Artificial Intelligence
Conglomerable coherence

International Journal of Approximate Reasoning
Kuznetsov independence for interval-valued expectations and sets of probability distributions: Properties and algorithms

International Journal of Approximate Reasoning

Quantified Score

Hi-index	0.21

Visualization

Abstract

We compare the different notions of conditional coherence within the behavioural theory of imprecise probabilities when all the spaces are finite. We show that the differences between the notions are due to conditioning on sets of (lower, and in some cases upper) probability zero. Next, we characterise the range of coherent extensions in the finite case, proving that the greatest coherent extensions can always be calculated using the notion of regular extension, and we discuss the extensions of our results to infinite spaces.