COMPOSITIONAL STATISTICAL MODELS UNDER A BAYESIAN APPROACH: AN APPLICATION TO TRAFFIC ACCIDENT DATA IN FEDERAL HIGHWAYS IN BRAZIL

ABSTRACT This study considers the use of a composicional statistical model under a Bayesian approach using Markov Chain Monte Carlo simulation methods applied for road traffic victims ocurring in federal roads of Brazil in a specified period of time. The main motivation of the present study is based on a database with information on the injury severity of each person involved in an accident occurred in federal highways in Brazil during a time period ranging from January, 2018 to April, 2019 reported by the federal highway police office of Brazil. Four types of events associated with each injured person (uninjured, minor injury, serious injury and death) are grouped for each state of Brazil in each month characterizing compositional multivariate data. Such kind of data requires specific modeling and inference approaches that differ from the traditional use of multivariate models assuming multivariate normal distributions.The proportion events associated to the accidents (uninjured, minor injuries, serious injuries and deaths) are considered as a sample of vectors of proportions adding to a value one together with some covariates such as pavement conditions in each province, regions of Brazil, months and years that may affect the severity of the injury of each person involved in an accident. From the obtained results, it is observed that the proportions of serious accidents and deaths are affected by some covariates as the different regions of Brazil and years.

摘要
本研究针对巴西联邦公路特定时段内发生的道路交通事故受害者，采用基于贝叶斯（Bayesian）框架的马尔可夫链蒙特卡洛（Markov Chain Monte Carlo, MCMC）模拟方法构建组成式统计模型开展相关研究。
本研究的核心动机源自巴西联邦公路警察局上报的数据库，该库涵盖2018年1月至2019年4月期间巴西联邦公路上发生的所有交通事故中涉事人员的伤情严重程度信息。针对每起交通事故中的涉事人员，共划分四类事件类型（未受伤、轻微伤、重伤及死亡），并按巴西各州及月度维度进行分组统计，由此形成组成式多元数据。此类数据需采用特定的建模与推断方法，与传统假设多元正态分布的多元模型框架存在显著差异。
本研究将每起交通事故对应的四类事件占比（未受伤占比、轻微伤占比、重伤占比及死亡占比）视为总和为1的比例向量样本，并纳入路面状况、巴西各行政区域、月份及年份等可能影响涉事人员伤情严重程度的协变量。研究结果显示，重伤及死亡事件占比会受到巴西不同行政区域及年份等协变量的影响。