Empirical Bayes Methods Applied to Estimating Fire Alarm Probabilities

Abstract An empirical Bayes approach is used to derive a Stein-type estimator of a multivariate normal mean when the components have unequal variances. This estimator is applied to estimating the probability that a fire alarm reported from a particular street box signals a structural fire rather than a false alarm 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 from yearly (1967–1969) Bronx data. A dispatching rule based on the estimates is evaluated on 1970 data.