A cross-comparison of different extreme value modeling techniques for traffic conflict-based crash risk estimation

A hybrid modelling framework of machine learning and extreme value theory for crash risk estimation using traffic conflicts

Random parameters Bayesian hierarchical modeling of traffic conflict extremes for crash estimation

Multi-type Bayesian hierarchical modeling of traffic conflict extremes for crash estimation

The block maxima approach is an important method in univariate extreme value analysis. While assuming that block maxima are independent results in straightforward analysis, the resulting inferences maybe invalid when a series of block maxima exhibits dependence. We propose a model, based on a first‐order Markov assumption, that incorporates dependence between successive block maxima through the use of a bivariate logistic dependence structure while maintaining generalized extreme value (GEV) marginal distributions. Modeling dependence in this manner allows us to better estimate extreme quantiles when block maxima exhibit short‐ranged dependence. We demonstrate via a simulation study that our first‐order Markov GEV model performs well when successive block maxima are dependent, while still being reasonably robust when maxima are independent. We apply our method to two polar annual minimum air temperature data sets that exhibit short‐ranged dependence structures, and find that the proposed model yields modified estimates of high quantiles.

Extreme value theory (EVT) is the branch of statistics concerned with inference about the tails of the distribution function. Accurate estimation of the year return levels of climate extremes is a critical step in the projection of future climate and in engineering design for disaster response. The study of non-stationary behavior in the extremes is important to analyze data in environmental sciences, climate, finance, or sports. The largest order statistics is an extension of the block maxima approach that is used in extreme value modeling. However, in Korea, the scientific literature usually has used the method based on fitting a distribution to an annual maximum. We focus on daily rainfall amounts data sets collected from the Korea Meteorological Administration for Seoul, Busan and Daegu, from 1961 to 2020. First, we fit the GEV df to block maxima data, i.e., annual maximum rainfall. Second, we use the top 10 annual precipitation events. We model, in which both mean and scale parameters of extreme value distribution are modeled as linear or smooth functions of covariate, YEAR, using the vector generalized linear models (VGLMs) and vector generalized additive models (VGAMs).

ABSTRACTThe block maxima approach, which consists of dividing a series of observations into equal‐sized blocks to extract the block maxima, is commonly used for identifying and modeling extreme events using the generalized extreme value (GEV) distribution. In the analysis of coastal wave surge levels, the underlying data that generate the block maxima typically have missing observations. Consequently, the observed block maxima may not correspond to the true block maxima, yielding biased estimates of the GEV distribution parameters. Various parametric modeling procedures are proposed to account for the presence of missing observations under a block maxima framework. The performance of these estimators is compared through an extensive simulation study and illustrated by an analysis of extreme wave surges in Atlantic Canada.

In the era of autonomous vehicles (AVs), accurately predicting extreme traffic conflicts is vital for improving road safety. This study leverages Extreme Value Theory (EVT) to analyse AV-generated conflict data, focusing on Modified Time-to-Collision (MTTC) and Post-Encroachment Time (PET) indicators. We compare univariate and bivariate EVT models using Peak-Over-Threshold (POT) and Block Maxima (BM) methods, addressing data’s spatiotemporal gaps. A novel model validation criterion is introduced, applicable across modeling approaches and sample sizes, independent of crash records. Results show bivariate POT models outperform univariate models by up to 20% lower Mean Absolute Error (MAE) and offer greater temporal stability. Univariate BM models are reliable only for short intervals (∼5–7 min), while POT models maintain or improve accuracy over time. Covariate selection significantly impacts model performance, varying by structure. Overall, bivariate POT models prove most effective, offering practical, adaptive tools for AV-based traffic conflict analysis in diverse urban environments.

Abstract. Extreme rainfall is classically estimated using raingauge data at raingauge locations. An important related issue is to assess return levels of extreme rainfall at ungauged sites. Classical methods consist in interpolating extreme-value models. In this paper, such methods are referred to as regionalization schemes. Our goal is to evaluate three classical regionalization schemes. Each scheme consists of an extreme-value model (block maxima, peaks over threshold) taken from extreme-value theory plus a method to interpolate the parameters of the statistical model throughout the Cévennes-Vivarais region. From the interpolated parameters, the 100-yr quantile level can be estimated over this whole region. A reference regionalization scheme is made of the couple block maxima/kriging, where kriging is an optimal interpolation method. The two other schemes differ from the reference by replacing either the extreme-value model block maxima by peaks over threshold or kriging by a neural network interpolation procedure. Hyper-parameters are selected by cross-validation and the three regionalization schemes are compared by double cross-validation. Our evaluation criteria are based on the ability to interpolate the 100-yr return level both in terms of precision and spatial distribution. It turns out that the best results are obtained by the regionalization scheme combining the peaks-over-threshold method with kriging.

In this paper, we survey some aspects of the relationship between random utility, extreme value theory and multinomial logit models. In particular, we study the robustness of the assumption of a Gumbel distributed random utility. These ideas are well known within the field of spatial economics, but do not appear to be common knowledge to researchers in probability theory. The purpose of this paper is to try to bridge this gap.

Safety analysis of passing maneuvers using extreme value theory

ABSTRACTObjective: Safety performance at bus stops is generally evaluated by using historical traffic crash data or traffic conflict data. However, in China, it is quite difficult to obtain such data mainly due to the lack of traffic data management and organizational issues. In light of this, the primary objective of this study is to develop a quantitative approach to evaluate bus stop safety performance.Methods: The concept of level-of-safety for bus stops is introduced and corresponding models are proposed to quantify safety levels, which consider conflict points, traffic factors, geometric characteristics, traffic signs and markings, pavement conditions, and lighting conditions. Principal component analysis and k-means clustering methods were used to model and quantify safety levels for bus stops.Results: A case study was conducted to show the applicability of the proposed model with data collected from 46 samples for the 7 most common types of bus stops in China, using 32 of the samples for modeling and 14 samples for illustration. Based on the case study, 6 levels of safety for bus stops were defined. Finally, a linear regression analysis between safety levels and the number of traffic conflicts showed that they had a strong relationship (R2 value of 0.908).Conclusions: The results indicated that the method was well validated and could be practically used for the analysis and evaluation of bus stop safety in China. The proposed model was relatively easy to implement without the requirement of traffic crash data and/or traffic conflict data. In addition, with the proposed method, it was feasible to evaluate countermeasures to improve bus stop safety (e.g., exclusive bus lanes).

A physics-informed road user safety field theory for traffic safety assessments applying artificial intelligence-based video analytics

Some events are difficult to avoid and gives considerable influence to humans and the environment is extreme weather and climate change. Many of the problems that require knowledge about the behavior of extreme values and one of the methods used are the Extreme Value Theory (EVT). EVT used to draw up reliable systems in a variety of conditions, so as to minimize the risk of a major disaster. There are two methods for identifying extreme value, Block Maxima with Generalized Extreme Value (GEV) distribution approach and Peaks over Threshold (POT) with Generalized Pareto Distribution (GPD) approach. This research in Indramayu with January 1961-December 2003 period, the method used is Block Maxima with GEV distribution approach. The result showed that there is no climate change in Indramayu with January 1961-December 2003 period.

Evt Caviar (Var Forecasts for Korea Treasurybonds Via Evt and Caviar Models)

Accurate forecasting of climate extremes such as floods, heatwaves, and severe storms is vital for risk mitigation and climate resilience planning. Traditional statistical models often fail to capture the nonlinear dynamics and tail dependencies inherent in such events. This paper proposes a novel hybrid framework that integrates Extreme Value Theory (EVT) with Deep Generative Models (DGMs), specifically Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs), for probabilistic modeling and simulation of rare climate phenomena. EVT is employed to model the marginal distributions of extreme events using the Generalized Pareto and Generalized Extreme Value distributions. Meanwhile, DGMs learn latent representations from high-dimensional climate data and synthesize realistic, tail-aware samples. The proposed model captures both the statistical rigor of EVT and the expressive power of deep learning. Empirical evaluations are conducted using ERA5 reanalysis and satellite datasets, focusing on extreme precipitation and temperature anomalies across diverse regions. Results show that the hybrid EVT–DGM framework significantly improves tail risk estimation, return level prediction, and generative quality compared to conventional models. This approach provides a robust tool for data-driven climate risk forecasting under uncertainty.