A Space–Time Conditional Intensity Model for Evaluating a Wildfire Hazard Index Roger D. PENG, Frederic Paik SCHOENBERG, and James A. WOODS Numerical indices are commonly used as tools to aid wildfire management and hazard assessment. Although the use of such indices is widespread, assessment of these indices in their respective regions of application is rare. We evaluate the effectiveness of the burning index (BI) for predicting wildfire occurrences in Los Angeles County, California using space–time point-process models. These models are based on an additive decomposition of the conditional intensity, with separate terms used to describe spatial and seasonal variability as well as contributions from the BI. We fit the models to wildfire and BI data from the years 1976–2000 using a combination of nonparametric kernel-smoothing methods and parametric maximum likelihood. In addition to using the Akaike information criterion (AIC) to compare competing models, we use new multidimensional residual methods based on approximate random thinning and rescaling to detect departures from the models and to ascertain the precise contribution of the BI to predicting wildfire occurrence. We find that although the BI appears to have a positive impact on wildfire prediction, the contribution is relatively small after taking into account natural seasonal and spatial variation. In particular, the BI does not appear to take into account increased activity during the years 1979–1981 and can overpredict during the early months of the year. KEY WORDS: Conditional intensity model; Model evaluation; Point process residual analysis; Random rescaling; Random thinning; Wildfire risk. 1. INTRODUCTION Fire departments all over the world often use numerical in- dices to aid wildfire management. These indices are designed to summarize local meteorological and fuel information and pro- vide an estimate of the current risk of fire. The burning index (BI) is part of the U.S. National Fire-Danger Rating System (NFDRS), a collection of numerical indices designed to be used for fire planning and management. The Los Angeles County Fire Department (LACFD) uses the BI for creating short-term wildfire hazard maps of the county that help managers make de- cisions involving the allocation of resources and coordination of presuppression activities. Although the BI is already in common use by Los Angeles and other fire departments, there have been relatively few at- tempts to assess the index’s performance in predicting wildfires. In the general area of index evaluation, there has been some work in evaluating elements of the U.S. system (e.g., Haines, Main, Frost, and Simard 1983) and various national (non-U.S.) systems (Viegas, Bovio, Ferreira, Nosenzo, and Sol 1999), and in using indices for prediction (Westerling, Cayan, Gershunov, Dettinger, and Brown 2000). However, the BI’s ability to adapt to particular regions, such as Los Angeles County, has yet to be fully scrutinized. Mandallaz and Ye (1997) have noted that in general, wildfire hazard indices are developed on the basis of experience in a given area. Therefore, one must take care when adapting indices to other areas. The aim of this article is to evaluate the performance of the BI in predicting wildfires in Los Angeles County. Our approach is Roger D. Peng is Postdoctoral Fellow, Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205 (E-mail: rpeng@jhsph.edu). Frederic Paik Schoenberg is Associate Professor, Depart- ment of Statistics, University of California, Los Angeles, CA 90095. James A. Woods is GIS Lab Manager and Instructor, Department of Geography, Cal- ifornia State University, Long Beach, CA 90840. This material is based on work supported by National Science Foundation grants 9978318 and 0306526. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. This work is part of the first author’s Ph.D. disser- tation from the University of California, Los Angeles. The authors thank Larry Bradshaw at the USDA Forest Service for providing the weather station data, as well as LADPW and LACFD (especially Mike Takeshita and Frank Vidales) for generously sharing their data and expertise. The associate editor and two reviewers provided valuable comments and suggestions that contributed to the revised manuscript. to evaluate the best-fitting conditional intensity model both with and without the BI and other information, not only to deter- mine the optimal use of the BI in point process prediction, but also to assess the increase in prediction performance using the BI as compared with other information. We compare the vari- ous conditional intensity models using the Akaike information criterion (AIC) as well as multidimensional residual analysis methods based on approximate random thinning and rescaling. Although the AIC proves useful for finding the best model in a set of possibilities, residual analysis can identify specific ar- eas where the performance is poor and suggest directions for improvement. In the sections that follow, we briefly describe the U.S. NFDRS and provide a summary of the data used for this analy- sis. We then outline the point-process methodology used for evaluating the performance of the BI. Finally, we discuss the results of applying these methods to the wildfire data from Los Angeles County, California. 2. A BRIEF SUMMARY OF THE NATIONAL FIRE–DANGER RATING SYSTEM The U.S. NFDRS was developed by the U.S. Department of Agriculture Forest Service in 1972 (Deeming, Lancaster, Fosberg, Furman, and Schroeder 1972) and was revised in 1978 (Deeming, Burgan, and Cohen 1977; Bradshaw, Deeming, Burgan, and Cohen 1983). Since then, there have been some adjustments (see, e.g., Burgan 1988). The NFDRS actually con- sists of multiple components that can be combined to form three different indices, of which the BI is one. Although this is a “national” system, there are many parameters that can be cali- brated to adapt the system to local environments. In particular, a fire manager must choose a fuel model (from a set of 20 avail- able models) that corresponds to the available fuel in the region. The fuel model is then incorporated into the index computations to produce an index for a specific region (Bradshaw et al. 1983). © 2005 American Statistical Association Journal of the American Statistical Association March 2005, Vol. 100, No. 469, Applications and Case Studies DOI 10.1198/016214504000001763 26