Measures of uncertainty in expert systems
Artificial Intelligence
Artificial Intelligence
The Art of Causal Conjecture
Annals of Mathematics and Artificial Intelligence
Updating beliefs with incomplete observations
Artificial Intelligence
Algorithmic Learning in a Random World
Algorithmic Learning in a Random World
Notes on conditional previsions
International Journal of Approximate Reasoning
Marginal extension in the theory of coherent lower previsions
International Journal of Approximate Reasoning
Graphical models for imprecise probabilities
International Journal of Approximate Reasoning
Imprecise markov chains and their limit behavior
Probability in the Engineering and Informational Sciences
Discrete time Markov chains with interval probabilities
International Journal of Approximate Reasoning
Epistemic irrelevance in credal nets: The case of imprecise Markov trees
International Journal of Approximate Reasoning
Concentration inequalities and laws of large numbers under epistemic and regular irrelevance
International Journal of Approximate Reasoning
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
Generalizing inference rules in a coherence-based probabilistic default reasoning
International Journal of Approximate Reasoning
Conglomerable natural extension
International Journal of Approximate Reasoning
A strong law of large numbers for non-additive probabilities
International Journal of Approximate Reasoning
Artificial Intelligence
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We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that (i) has an interesting interpretation, and (ii) allows us to freely import results from one theory into the other. Our approach leads to an account of probability trees and random processes in the framework of Walley's theory. We indicate how our results can be used to reduce the computational complexity of dealing with imprecision in probability trees, and we prove an interesting and quite general version of the weak law of large numbers.