2014/08/07 by Gert de Cooman, de Cooman, Gert, Marco Zaffalon +1
Computer Science · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic #cs.AI
paper · pdf · doi:10.48550/arxiv.1408.1488
Appears in Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence (UAI2003)
arxiv created 2014/08/07 · openalex publication_date 2014/08/07 · arxiv updated 2014/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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, and of particular interest for Bayesian networks. Recently, Grunwald and Halpern have shown that commonly used updating strategies fail here, except under very special assumptions. We propose a new rule for updating probabilities with incomplete observations. Our approach is deliberately conservative: we make no or weak assumptions about the so-called incompleteness mechanism that produces incomplete observations. We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we derive a new updating rule using coherence arguments. In general, our rule produces lower posterior probabilities, as well as partially determinate decisions. This is a logical consequence of the ignorance about the incompleteness mechanism. We show how the new rule can properly address the apparent paradox in the 'Monty Hall' puzzle. In addition, we apply it to the classification of new evidence in Bayesian networks constructed using expert knowledge. We provide an exact algorithm for this task with linear-time complexity, also for multiply connected nets.