Statistical analysis with missing data
Statistical analysis with missing data
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Knowledge, probability, and adversaries
Journal of the ACM (JACM)
Measures of uncertainty in expert systems
Artificial Intelligence
2U: an exact interval propagation algorithm for polytrees with binary variables
Artificial Intelligence
Artificial Intelligence
Robust Learning with Missing Data
Machine Learning
Strong Conditional Independence for Credal Sets
Annals of Mathematics and Artificial Intelligence
Separation Properties of Sets of Probability Measures
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
A new approach to updating beliefs
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Journal of Artificial Intelligence Research
Inference with separately specified sets of probabilities in credal networks
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Learning from what you don't observe
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Updating with incomplete observations
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Fast algorithms for robust classification with Bayesian nets
International Journal of Approximate Reasoning
Decision making under incomplete data using the imprecise Dirichlet model
International Journal of Approximate Reasoning
Marginal extension in the theory of coherent lower previsions
International Journal of Approximate Reasoning
A survey of the theory of coherent lower previsions
International Journal of Approximate Reasoning
Imprecise probability trees: Bridging two theories of imprecise probability
Artificial Intelligence
International Journal of Approximate Reasoning
Statistical matching of multiple sources: A look through coherence
International Journal of Approximate Reasoning
Representation insensitivity in immediate prediction under exchangeability
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Updating coherent previsions on finite spaces
Fuzzy Sets and Systems
Modeling Unreliable Observations in Bayesian Networks by Credal Networks
SUM '09 Proceedings of the 3rd International Conference on Scalable Uncertainty Management
Conservative inference rule for uncertain reasoning under incompleteness
Journal of Artificial Intelligence Research
Partial identification with missing data: concepts and findings
International Journal of Approximate Reasoning
Graphical models for imprecise probabilities
International Journal of Approximate Reasoning
Credal semantics of Bayesian transformations in terms of probability intervals
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Epistemic irrelevance in credal nets: The case of imprecise Markov trees
International Journal of Approximate Reasoning
Notes on desirability and conditional lower previsions
Annals of Mathematics and Artificial Intelligence
Incoherence correction strategies in statistical matching
International Journal of Approximate Reasoning
Likelihood-based Imprecise Regression
International Journal of Approximate Reasoning
Partially identified prevalence estimation under misclassification using the kappa coefficient
International Journal of Approximate Reasoning
Artificial Intelligence
Safe probability: restricted conditioning and extended marginalization
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Belief function and multivalued mapping robustness in statistical estimation
International Journal of Approximate Reasoning
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Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or set-valued). This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently, Grünwald and Halpern have shown that commonly used updating strategies fail in this case, except under very special assumptions. In this paper we propose a new method for updating probabilities with incomplete observations. Our approach is deliberately conservative: we make no assumptions about the so-called incompleteness mechanism that associates complete with incomplete observations. We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we use only coherence arguments to turn prior into posterior (updated) probabilities. In general, this new approach to updating produces lower and upper posterior probabilities and previsions (expectations), as well as partially determinate decisions. This is a logical consequence of the existing ignorance about the incompleteness mechanism. As an example, we use the new updating method to properly address the apparent paradox in the 'Monty Hall' puzzle. More importantly, we apply it to the problem of classification of new evidence in probabilistic expert systems, where it leads to a new, so-called conservative updating rule. In the special case of Bayesian networks constructed using expert knowledge, we provide an exact algorithm to compare classes based on our updating rule, which has linear-time complexity for a class of networks wider than polytrees. This result is then extended to the more general framework of credal networks, where computations are often much harder than with Bayesian nets. Using an example, we show that our rule appears to provide a solid basis for reliable updating with incomplete observations, when no strong assumptions about the incompleteness mechanism are justified.