Bivariate extreme value modeling for road safety estimation

This study investigates left-turn safety at urban intersections using surrogate safety measures derived from field video observations. Time-to-Collision (TTC) among motorized traffic and Post-Encroachment Time (PET) among pedestrian and motorized traffic were extracted for left-turn conflicts across five intersection types in Thessaloniki, Greece, and linked to geometric attributes, signal operations, and traffic conditions. Count-based models (Poisson, Negative Binomial) were estimated alongside machine-learning approaches (Random Forest, Gradient Boosting with Poisson loss). For PET events, the Poisson model had the best balance of parsimony and predictive accuracy, whereas the Negative Binomial model provided a superior fit for TTC events. Results indicate that PET-defined conflicts increased with pedestrian volume and the presence of shared and protected left-turn lanes, and decreased with higher opposing flow, greater average acceleration, and wider end-approach lanes. By contrast, TTC events were associated with lower average speeds, the presence of protected signal phasing for left turns, and the number of passenger cars. Machine-learning models underperformed relative to classical count models, reflecting limited sample size and the discrete event structure. The analysis indicates that the determinants of TTC and PET differ, with certain variables such as pedestrian activity and lane configuration having contrasting effects on the two surrogate safety measures. The analysis reveals that pedestrian demand and shared lane configurations significantly increase PET occurrences, whereas TTC events are more strongly associated with vehicle volumes, speeds, and signal phasing. This distinction underscores the importance of tailoring safety assessment and intervention strategies to the type of interaction being evaluated.

Most safety analysis is conducted using crash data. Surrogate safety measures, such as various time-based measures of time-to-collision can be related to crash potential and used to gain insight into the frequency and severity of crashes at a specific location. One of the most common and acknowledged measures is post-encroachment time (PET) which defines the time between vehicles occupying a conflicting space. While commonly used in studies of motor vehicle interactions, studies of PET for bicycle-vehicle interactions are few. In this research, the PET of bicycle-vehicle interactions measured in the field, a driving simulator, and in a micro-simulation are compared. A total of 52 right-hook conflicts were identified in 135 hours of video footage over 14 days at a signalized intersection in Portland, OR (SW Taylor and SW Naito Pkwy). The results showed that 4 of 17 high-risk conflicts could not be identified by the conventional definition of PET and PET values of some conflicts did not reflect true risk of collision. Therefore, right-hook conflicts were categorized into two types and a modified measure of PET was proposed so that their frequency and severity were properly measured. PETs from the field were then compared to those measures in the Oregon State University driving simulator during research conducted by Dr. Hurwitz et al. (2015) studying the right-hook conflicts. Statistical and graphical methods were used to compare field PETs to those in the simulator. The results suggest that the relative validity of the OSU driving simulator was good but not conclusive due to differences in traffic conditions and intersections. To further explore the field-observed PET values, traffic simulation models of the field intersection were developed and calibrated. Right-hook conflicts were extracted from the simulation files and conflicts observed in PM-peak hours over 6 days in the field were compared to those obtained from 24 traffic simulation runs. The field-observed PET values did not match the values from the simulation values very well. However, the approach does show promise. Further calibration of driving and bicycling behaviors would likely improve the result.

Multivariate Bayesian hierarchical modeling of the non-stationary traffic conflict extremes for crash estimation

The Development of Conflict Index for the Safety Assessment of Intersections Considering Crash Probability and Severity

Fusing crash data and surrogate safety measures for safety assessment: Development of a structural equation model with conditional autoregressive spatial effect and random parameters

In the developing world, with increases in population, the number of vehicles is increasing tremendously. Traffic safety on roads has become a major concern even with advancements in technology and infrastructure. Traffic safety assessments and accident prediction based on accident data is a reactive approach. There are known drawbacks related to the reliability of accident data, especially in developing countries with large populations, such as India. It is, however, unethical to wait for accidents to occur before drawing statistically accurate conclusions regarding safety impacts. To overcome this impediment, one needs to develop accurate models that rely on surrogate safety measures (SSMs) for effective safety evaluations. The main advantage associated with the use of these models is that they can model crashes more frequently than in the real world and thereby imply an efficient and more statistically reliable proximal measure of traffic safety. The objective of this study is to examine the impact of management measures on traffic safety at a three-arm uncontrolled intersection with the use of microsimulation modeling under mixed traffic conditions. This examination was done by developing a unique methodology of measuring one SSM, postencroachment time (PET). This paper describes improvement in the accuracy of crash predictions by proposing a methodology to calculate PET.

The implications of situation and route familiarity for driver-pedestrian interaction at uncontrolled mid-block crosswalks

This study aims to investigate the different behaviors with respect to safety measures related to the interaction of e-scooters and bikes with cars in mixed traffic. E-scooters are relatively new vulnerable road users, and their behavior is still not fully understood. For this purpose, an observational study was carried out at an unsignalized at-grade intersection in the city of Catania, Italy. A total of 128 interactions between cars and e-scooters and 89 interactions between cars and bikes were detected. Specifically, two surrogate measures of safety were used, the time to collision (TTC) and post encroachment time (PET), which relate to the “crossing” and the “following” interactions between cars and bikes/e-scooters. The results show that 50% of the “crossings” involving bikes were close interactions with low TTCs representing high risk (TTC < 1.5); meanwhile, for the “crossing” interactions between cars and e-scooters, the same threshold of TTC relates to percentiles of more than 80%. In addition, more than 60% of interactions between cars and e-scooters were characterized by PET values representing a potentially high risk (PET < 1.0 s). The results provide a useful starting point for the elaboration and adaptation of new regulations for mixed traffic conditions including e-scooters that are currently being introduced in several countries with different rules. It should be noted that e-scooters are an intrinsically different transport mode from a bicycle, mainly because their interactions in mixed traffic show that they are prone to a higher risk of closer interactions.

Pedestrians and vehicles frequently interact at signalized intersections, where many pedestrian crashes involve right-turning vehicles. Toward improving safety, it is essential to understand the factors influencing pedestrian–vehicle interactions and conflicts. Using post-encroachment time (PET) as a surrogate safety measure, this study investigated associations of various conflict- and location-specific factors with pedestrian conflict severity, and ascertained variations across locations. Data were collected for 639 pedestrian–right-turn vehicle conflicts observed from over 1,000 hours of video at 33 intersections in Utah. Next, correlations were calculated and multilevel models (conflicts nested within intersections) were estimated. Conflicts tended to be more severe (shorter PET) when pedestrians were younger, men, leaving the curb, and using the second crosswalk that drivers encounter when turning right. Conversely, conflicts were less severe (longer PET) for women, those using strollers or wheelchairs, and pedestrians approaching the curb or using the first crosswalk. Concerning traffic signal operations, more severe conflicts occurred when vehicles were turning right on green and when pedestrians were crossing against a “Steady Don’t Walk” indication. Conflicts tended to be slightly less severe at locations with larger corner radii, high-visibility crosswalk markings, shared thru/right-turn lanes, channelized and unsignalized right-turn lanes, nonskewed intersections, and more pedestrian volumes. These results offer practical implications, such as using corner geometry and continental crosswalk markings to increase visibility between pedestrians and drivers, or considering warning signs, leading pedestrian intervals, and prohibiting right-turns-on-red in some locations. Agencies can leverage these insights to reduce conflict severity and advance Vision Zero safety goals for pedestrians.

A study on estimation and prediction in bivariate geostatistical models Bivariate geostatistical models dene random functions for two stochastic processes with known spatial locations. Existence of a Gaussian random elds can be assumed for each latent random variable. This Gaussianity assumption for the latent process is a convenient one for the inferences on the model parameters and for spatial predictions once the joint distribution for a set of points is multivariate normal. The covariance matrix of this distribution should be positivedenite and to have the spatial variability structure between and among the attributes. Gelfand et al. (2004) and Diggle e Ribeiro Jr. ( This work reports on a simulation study of bivariate models together with maximum likelihood estimators and spatial prediction under dierent sets of sampling locations space. Soil sample data from a eld with 51.8 hectares is also analyzed with the two soil attributes observed at 67 spatial locations. Data on pH and base saturation were submitted to spatial descriptive analysis, univariate and bivariate modeling and spatial prediction. To check for advantages of the adoption of univariate or bivariate models, the sample of the more expensive variable was divided into a modeling and testing subsamples. The rst was used to t geostatistical models, and the second was used to compare the spatial prediction precisions in the locations not used in the modeling process.

To identify the genetic determinants of obesity using univariate and bivariate models in a genome scan. We evaluated the genetic and environmental effects and performed a genome-wide linkage analysis of obesity-related traits in 478 subjects from 105 Mexican-American nuclear families ascertained through a proband with documented coronary artery disease. The available obesity traits include BMI, body surface area (BSA), waist-to-hip ratio (WHR), and trunk fat mass as percentage of body weight. Heritability estimates and multipoint linkage analysis were performed using a variance components procedure implemented in SOLAR software. The heritability estimates were 0.62 for BMI, 0.73 for BSA, 0.40 for WHR, and 0.38 for trunk fat mass as percentage of body weight. Using a bivariate genetic model, we observed significant genetic correlations between BMI and other obesity-related traits (all p < 0.01). Evidence for univariate linkage was observed at 252 to approximately 267 cM on chromosome 2 for three obesity-related traits (except for WHR) and at 163 to approximately 167 cM on chromosome 5 for BMI and BSA, with the maximum logarithm of the odds ratio score of 3.12 (empirical p value, 0.002) for BSA on chromosome 2. Use of the bivariate linkage model yielded an additional peak (logarithm of the odds ratio = 3.25, empirical p value, 0.002) at 25 cM on chromosome 7 for the pair of BMI and BSA. The evidence for linkage on chromosomes 2q36-37 and 5q36 is supported both by univariate and bivariate analysis, and an additional linkage peak at 7p15 was identified by the bivariate model. This suggests that use of the bivariate model provides additional information to identify linkage of genes responsible for obesity-related traits.

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.

Data comprising 7211 lactation records of 2894 cows were used to estimate genetic and phenotypic parameters for milk production (lactation milk yield, LMY and lactation length, LL) and fertility (calving interval, CI; number of services per conception, NSC and age at first calving, AFC) traits. Genetic, environmental and phenotypic trends were also estimated. Variance components were estimated using univariate, bivariate and trivariate animal models on based restricted maximum likelihood procedures. Univariate models were used for each trait, while bivariate models were used to estimate genetic and phenotypic correlations between milk production and fertility traits and between LMY, LL, CI and NSC within each lactation. Trivariate models were used in the analysis of LMY, LL, CI and NSC in the first three lactations. Heritability estimates from the univariate model were 0.16, 0.07, 0.03, 0.04 and 0.01 for LMY, LL, CI, AFC and NSC, respectively. The heritability estimates from trivariate analysis were higher for milk production traits than those from univariate analyses. Genetic correlations were high and undesirable between milk production and fertility traits, while phenotypic correlations were correspondingly low. Genetic trends were close to zero for all traits, while environmental and phenotypic trends fluctuated over the study period.

Multivariate Bayesian hierarchical Gaussian copula modeling of the non-stationary traffic conflict extremes for crash estimation

The focus of traffic safety research has recently shifted from reactive to proactive safety management approaches. In reactive approaches, historical crash data is used to identify accident-prone locations or black spots. However, this approach is inherently reactive, focusing on accidents that have already occurred, requiring several years of accident data. Recently, surrogate safety measures have been adopted as a proactive alternative for identifying black spots. Nowadays, the widespread use of smartphones equipped with GPS systems makes it possible to utilize mobile GPS data to identify accident-prone locations. In this study, GPS-derived surrogate safety measures extracted from smartphone data are used to predict the frequency of potential accident incidences on road segments. On this basis, several Poisson-based statistical models and Artificial Neural Network (ANN) models were developed based on the data collected by smartphones on two carriageways of a long arterial street in Mashhad, Iran. GPS trajectory data, including vehicle speed, acceleration, and location, were collected using a GPS data recorder application installed on the smartphones of drivers and passengers traveling along the carriageway. The results indicated that both the Poisson-based and ANN models can predict crash frequency with reasonable accuracy. However, the ANN model, comprising surrogate speed and acceleration-related safety measures, demonstrated slightly better performance than Poisson-based regression models. The models were then successfully tested for their ability to identify accident-prone segments. Our findings indicated that data obtained from smartphones can be used as surrogate measures for assessing road safety and ranking accident-prone segments along urban roads.