New York City Fire Alarm Prediction Models

Four models for estimating the probability that a box-reported alarm signals a serious fire are given and compared: (1) One-Stage Box History; (2) One-Stage Empirical Bayes; (3) Two-Stage Empirical Bayes Binomial; (4) Two-Stage Empirical Bayes Constant Over Region. Estimates were calculated from data of all alarm boxes in the Bronx prior to and including 1969, and then evaluated by comparison with 1970 data. Estimates were first compared by using a standard statistical test. In addition, estimates were evaluated by comparing the results of dispatching policies based on each of the estimates. Using both the statistical test and the comparison of dispatch policies, it was found that (1) empirical Bayes estimates perform better than estimates based only on the history of the box signaling the alarm, and (2) two-stage estimates are superior to one-stage estimates. That is, in predicting the probability of a serious fire, it is better to first predict the probability of a fire in an occupied structure and then predict the probability that the occupied structural fire is serious, rather than attempt to predict the probability of a serious fire directly.