Fire service response to fire is premised on the assumption that the earlier the fire is attacked the smaller will be the consequences to people and property. A simple method is shown for measuring the influence fire service response has on building fire development. The results for New Zealand are shown. The method is then extended to determining a nominal monetary benefit from rapid response and benefits in terms of other desired outcomes. The method allows the benefits of monitored fire alarms and sprinklers to be quantified. Finally the method is extended to determining the impact on fire service response of calls from cellular phones versus standard landlines. In the New Zealand circumstances the use of cellular phones does not appear on average to provide a speedier alert to the fire service and generally involves a marginally slower response owing to delays in locating incidents. This results in a measurably greater monetary loss.

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A new family of tree models is proposed, which we call "differential trees." A differential tree model is constructed from multiple data sets and aims to detect distributional differences between them. The new methodology differs from the existing difference and change detection techniques in its nonparametric nature, model construction from multiple data sets, and applicability to high-dimensional data. Through a detailed study of an arson case in New Zealand, where an individual is known to have been laying vegetation fires within a certain time period, we illustrate how these models can help detect changes in the frequencies of event occurrences and uncover unusual clusters of events in a complex environment.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS548 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org