Calculating uncertainty intervals from conditional convex sets of probabilities
UAI '92 Proceedings of the eighth conference on Uncertainty in Artificial Intelligence
Updating beliefs with incomplete observations
Artificial Intelligence
The Dempster--Shafer calculus for statisticians
International Journal of Approximate Reasoning
Limits of learning about a categorical latent variable under prior near-ignorance
International Journal of Approximate Reasoning
Conservative inference rule for uncertain reasoning under incompleteness
Journal of Artificial Intelligence Research
International Journal of Approximate Reasoning
Imprecise probabilities for representing ignorance about a parameter
International Journal of Approximate Reasoning
Inference about constrained parameters using the elastic belief method
International Journal of Approximate Reasoning
Mathematical foundations for a theory of confidence structures
International Journal of Approximate Reasoning
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We consider the case in which the available knowledge does not allow to specify a precise probabilistic model for the prior and/or likelihood in statistical estimation. We assume that this imprecision can be represented by belief functions models. Thus, we exploit the mathematical structure of belief functions and their equivalent representation in terms of closed convex sets of probabilities to derive robust posterior inferences using Walley@?s theory of imprecise probabilities. Then, we apply these robust models to practical inference problems and we show the connections of the proposed inference method with interval estimation and statistical inference with missing data.