Fire Hazard Estimation Using Point Process Methods

拟议的研究的目的是调查估计火灾的危险性在洛杉矶盆地使用多变量点过程分析技术。 该策略是模型火灾发生作为一个显着的时空点过程，其条件率不仅取决于以前的火灾记录，但对其他协变量以及。 这些协变量包括当地环境因素，如温度、海拔、湿度、降水、植被和土壤特性。 这项研究的一个重要组成部分是通过似然分析（根据过去的数据）和预测性能的评价（使用模型拟合后获得的数据）评估各种不同的模型。 使用该模型，表现最好的，调查人员打算构建定量预测的本地火灾危险伴随着这些预测的不确定性估计。 他们还计划将这些预测的危险综合起来，形成详细的、定期更新的洛杉矶盆地内火灾风险图，并将这些危险图和相应的当地危险估计数字公布在万维网上，供科学家同行和公众使用。 调查人员的方法对研究洛杉矶火灾危险以外的其他各种领域的科学家也很感兴趣。统计兴趣是使用现代技术在点过程理论，如应用多维分支，马尔可夫，和多阶段的点过程模型和使用多维随机时间变化定理在评估这些模型。 此外，分析中使用的方法不仅适用于获得其他地区火灾危险的估计，而且适用于量化类似类型的危险事件，包括洪水，风暴，飓风，龙卷风，地震，火山，海啸，疾病流行等。美国历史上一些最具破坏性的自然灾害都是由野火造成的。 然而，迄今为止，对火灾威胁的研究缺乏足够的科学审查和数学精确度。这项拟议研究的直接实际目标是获得和传播当地对洛杉矶县野火危害的详细估计。基本战略是利用当地火灾发生的趋势以及火灾发生率与其他环境因素之间的关系。 由此产生的火灾危险估计，以及火灾发生率和其他变量之间发现的关系，需要在城市和研究如何最好地减轻火灾的潜在灾难性影响和附近的城市地区。 特别值得关注的是，公共政策，如积极的灭火和规定的燃烧对火灾发生率和整体火灾危险的影响。该项目是由数学科学司统计计划和多学科活动办公室在MPS联合支持。

The intent of the proposed research is to investigate the estimation of fire hazard in the Los Angeles basin using techniques from multivariate point process analysis. The strategy is to model fire occurrence as a marked spatial-temporal point process whose conditional rate depends not only on the record of previous fires but on other covariates as well. These covariates include local environmental factors such as temperature, altitude, humidity, precipitation, vegetation, and soil characteristics. An important component of this research is the assessment of various different models via likelihood analysis (based on past data) and the evaluation of forecasting performance (employing data obtained after the models are fitted). Using the model, which performs best, the investigators intend to construct quantitative predictions of local fire hazard accompanied by estimates of uncertainties in these predictions. They also plan to integrate these predicted hazards to form detailed, regularly-updated, maps of the risk of fire within the Los Angeles basin and to make these hazard maps and corresponding numerical local hazard estimates available to fellow scientists and to the public by posting the results, with appropriate explanations, on the World Wide Web. The investigators' methodology is of interest to scientists studying various other fields besides fire hazard in Los Angeles. Of statistical interest is the use of modern techniques in point process theory such as the application of multi-dimensional branching, Markovian, and multi-stage point process models and the use of the multi-dimensional random time change theorem in assessing such models. In addition, the methods used in the analysis is applicable not only in obtaining estimates of fire hazard in other regions, but also in quantifying similar types of dangerous occurrences, including floods, storms, hurricanes, tornadoes, earthquakes, volcanoes, tsunamis, disease epidemics, etc.Some of the most devastating natural disasters in the history of the UnitedStates have been caused by wildfires. However, the threat of fire has been examined with insufficient scientific scrutiny and mathematical precision to date. The immediate practical goal of this proposed research is to obtain and disseminate detailed local estimates of the hazard from wildfires in Los Angeles County. The basic strategy is to exploit local trends in fire occurrence and relationships between the incidence of fires and other environmental factors. The resulting fire hazard estimates, as well as the relationships discovered between fire incidence and other variables, are needed in urban and in the study of how best to mitigate the potentially disastrous effects of fires in and near urban areas. Of particular concern is the effect of public policies such as aggressive fire suppression and prescribed burning on fire occurrence rate and overall fire hazard.This project is jointly supported by the Statistics Program in the Division of Mathematical Sciences and the Office of Multidisciplinary Activities in MPS.