KSL-91-49
## Modeling time in belief networks

**Reference: **
Dagum, P.;
Shachter, R.; &
Fagan, L. Modeling time in belief networks. Knowledge Systems Laboratory, November, 1991.

**Abstract:**
This report addresses the problem of modeling time in dynamic domains given
incomplete and uncertain information about the domain. Our first objective is
to construct a dynamic model within a belief-network paradigm and to
demonstrate how well-known time series concepts--such as backward smoothing,
forward filtering and forecasting--are implemented in this model.
The dynamic model is generated semiautomatically given a belief network that
models the time-invariant relations of the domain. Thus we have a
semiautomatic method for extending existing belief network models to dynamic
belief-network models that can be used in applications where consideration of
the time evolution of system variables is crucial to making valid inferences
about the domain. The second objective is to design an efficient randomized
approximation scheme (RAS) for probabilistic inference in belief networks to
be employed by our dynamic model.
Certain features unique to a RAS, compared to other stochastic simulation
algorithms for probabilistic inference, make the RAS desirable as an inference
algorithm for a dynamic model. For example, in dynamic domains, the time
required to make a decision enters the utility of the decision when this time
becomes comparable to the expected time in which the system changes
sufficiently to outdate a decision. A RAS provides an a priori bound on the
running time required to achieve a predefined level of accuracy in the
output. This information can be used to reduce the loss of utility due to
delayed decisions. Existing RASs for probabilistic inference in belief
networks are known to have a poor worst-case behavior. The class of belief
networks for which existing RASs run efficiently have been characterized in
previous research.
We optimize the RAS specifically for computing inferences in the dynamic
models.

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