A generalization of empirical Bayes estimators to the case in which the components have unequal variance. This estimator is applied to the spatial analysis problem of estimating the probability that a fire alarm reported from a particular street box signals a structural fire rather than a false alarm, rubbish fire or other emergency. The approach is to group alarm boxes into relatively homogeneous neighborhoods and to make empirical Bayes estimates of the "probability structural" for each box in the neighborhood for yearly (1967-1969) Bronx data. The results are evaluated by measuring how a dispatching rule based on the estimates performs on 1970 data. (Basic research on an OEO grant; for publication in the [Journal of the American Statistical Association].) 25 pp. Ref.