Updating with incomplete observations

Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or setvalued). This is a fundamental problem, and of particular interest for Bayesian networks. Recently, Gr¨unwald 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 ...

• Type: Conference
• Year: 2003
• Where: UAI
• Authors: Gert de Cooman, Marco Zaffalon
• Keywords: Bayesian Networks, Incomplete Observations, Incompleteness Mechanism, UAI 2003, UAI 2008