Probabilistic reasoning with temporal indeterminacy

Temporal indeterminacy, the lack of specific knowledge about the timing of events, occurs often in temporal reasoning in practical applications and is connected to the concept of time granularity. Although logical properties of granularities have been described by several researchers in the literature, the implications of temporal indeterminacy and granularities for probabilistic representation and reasoning have received little attention. Given the widespread occurrence of problems, specifically in medicine, where one has to cope with both temporal indeterminacy and uncertainty, it is somewhat surprising that methods that handle both do not exist as yet. In this paper we propose a formalism to model granularities in temporal Bayesian networks in order to deal with temporal indeterminacy in predictive Bayesian-network models. In addition, some of the properties of multigranular models are explored. Finally, we study a medical use case.