A hierarchical Bayesian model for predicting fire ignitions after an earthquake with application to California

Fire following earthquake is a major threat to communities in seismic-prone areas. For mitigation and preparedness against this multi-hazard event, predictive models are needed starting with the expected number of ignitions. Previous studies have proposed regression models calibrated on historical data for predicting post-earthquake ignitions; however, the data scarcity due to low frequency of major earthquakes has been a hurdle for building these regression models. To address this issue, this paper proposes the use of hierarchical Bayesian modeling to analyze the influential variables affecting the number of past ignitions and to predict the number of ignitions of future earthquakes. The data comes from seven major earthquakes that occurred in California, for which the number of ignitions and corresponding variables were collected from fire department reports and GIS-based inventory. The collected data were randomly divided into a calibration dataset and a validation dataset for building the model. The results indicate that the hierarchical Bayesian model efficiently extracts the significant influential variables and shows agreement with the number of ignitions after each of the seven earthquakes. The posterior predictions from the hierarchical Bayesian model also provide uncertainty quantification for the estimates of the ignitions after each earthquake. The proposed model is then applied to a hypothetical magnitude 7.0 earthquake scenario along the Hayward Fault to illustrate applicability for community resilience assessment.