The performance of probabilistic information retrieval systems is stud
ied where differing statistical dependence assumptions are used when e
stimating the probabilities inherent in the retrieval model. Experimen
tal results using the Bahadur Lazarsfeld expansion suggest that the gr
eatest degree of performance increase is achieved by incorporating ter
m dependence information in estimating Pr (d\rel). It is suggested tha
t incorporating dependence in Pr (d\rel) to degree 3 be used; incorpor
ating more dependence information results in relatively little increas
e in performance. Experiments examine the span of dependence in natura
l language text, the window of terms in which dependencies are compute
d, and their effect on information retrieval performance. Results prov
ide additional support for the notion of a window of +/- 3 to +/- 5 te
rms in width; terms in this window may be most useful when computing d
ependence.