Extreme Value Approach Research Articles

Defining Traffic Conflict in Nonlane-Based Traffic Conditions: An Extreme Value Approach

Defining Traffic Conflict in Nonlane-Based Traffic Conditions: An Extreme Value Approach

Extreme-value modelling of the brightest galaxies at z ≳ 9

Abstract Data from the James Webb Space Telescope have revealed an intriguing population of bright galaxies at high redshifts. In this work, we use extreme-value statistics to calculate the distribution (in UV magnitude) of the brightest galaxies in the redshift range 9 ≲ z ≲ 16. We combine the Generalised Extreme Value (GEV) approach with modelling of the galaxy luminosity function. We obtain predictions of the brightest galaxies for a suite of luminosity functions, including the Schechter and double power law functions, as well as a model parametrised by the stellar formation efficiency f*. We find that the JWST data is broadly consistent with f* of $5~{{\ \rm per\ cent}}-10~{{\ \rm per\ cent}}$, and that the brightest galaxy at z ∼ 16 will have $M_{\rm UV}\approx -23.5^{0.8}_{0.4}$. If f* is dependent on halo mass, we predict $M_{\rm UV}\approx -22.5^{0.5}_{1.5}$ for such an object. We show that extreme-value statistics not only predicts the magnitude of the brightest galaxies at high redshifts, but may also be able to distinguish between models of star formation in high-redshift galaxies.

Estimating crash risk and injury severity considering multiple traffic conflict and crash types: A bivariate extreme value approach

Traffic conflicts are generally considered independent events in existing extreme value theory models to estimate the risk of total or single types of crashes. However, traffic events at a road entity are not necessarily independent interactions and can lead to multiple traffic conflicts with shared common unobserved factors. A comprehensive estimation of crash risks in a road entity needs to consider the correlation of potential traffic conflicts to avoid possible bias in prediction performance and the problem of undetected deficiencies. This study proposes a Bayesian non-stationary bivariate generalised extreme value modelling framework to estimate the severe and non-severe crash risks accounting for the correlation between right-turn and rear-end conflicts at signalised intersections. A deep neural network-based computer vision technique was applied to extract the traffic conflicts from 77 h of video recordings over two right-turn approaches at two signalised intersections in Cairns, Australia. Post encroachment time and modified time to collision were used to characterise right-turn and rear-end conflicts, respectively, while an expected post-collision velocity difference was combined with post encroachment time and modified time to collision for crash risk estimation by injury severity levels. Several covariates were used to address the time-varying heterogeneity of traffic conflict extremes and to estimate the differential crash risks at signal cycles. Results showed a significant correlation between right-turn and rear-end crashes at signal cycle levels, indicating the importance of accounting for the dependency among traffic conflict types. Overall, the bivariate models considering the correlation among traffic conflict types were found to understandably perform better than their univariate counterparts. This study provides a demonstration of a correlated crash risk modelling framework that addresses issues related to the suitable traffic conflict measures, time varying risks (non-stationarity), heterogeneity, and injury severity levels of different crash types.

Modeling rainfall extremes along the coastal and Northern parts of Ghana

The main objective of the study was to determine the appropriate distribution for extreme rainfall along the coastal and northern sectors of Ghana. For stakeholders and policymakers to make appropriate risk-mitigating measures to lessen the damage caused by flood and drought, it is necessary to make proper inferences about extreme rainfall. In this study, we used both the multivariate and univariate extreme value data analysis approaches. The Generalized Extreme Value (GEV) with the Block Maxima approach and Generalized Pareto Distribution (GPD) with the Peak over the threshold (that is all excesses and decluster peaks approaches) were used in this study. Historical gridded monthly maximum rainfall data from 1970 to 2020 were obtained from the Climatic Research Unit and were grouped as the coastal and northern stations. The Maximum Likelihood Estimation method was used to estimate the model parameters, and both the unit root test and the Mann-Kendall tests were used to test for trend in the data. With the multivariate extreme modelling approach, the logistic bivariate GEV model was chosen as the “best” model. However, the dependence value was 0.965, so the extreme rainfall should be modelled independently using the univariate extreme value approaches. Hence, based on the information criteria and analysis of deviance approaches, the GEV distribution was considered the “best” fit for the extreme rainfall dataset for the northern part of Ghana. In contrast, the GPD distribution was the “best” fit for the coastal station. Comparatively, for the volume of rainfall in the year 2020, the extreme rainfall is expected to be higher in the coastal station of Ghana in the next two years. Also, extreme rainfall in 2 years would not exceed the maximum occurrence of rainfall (279.267), which happened in September 2020 at the northern station of Ghana.

Estimating cutoff values for diagnostic tests to achieve target specificity using extreme value theory

BackgroundRapidly developing tests for emerging diseases is critical for early disease monitoring. In the early stages of an epidemic, when low prevalences are expected, high specificity tests are desired to avoid numerous false positives. Selecting a cutoff to classify positive and negative test results that has the desired operating characteristics, such as specificity, is challenging for new tests because of limited validation data with known disease status. While there is ample statistical literature on estimating quantiles of a distribution, there is limited evidence on estimating extreme quantiles from limited validation data and the resulting test characteristics in the disease testing context.MethodsWe propose using extreme value theory to select a cutoff with predetermined specificity by fitting a Pareto distribution to the upper tail of the negative controls. We compared this method to five previously proposed cutoff selection methods in a data analysis and simulation study. We analyzed COVID-19 enzyme linked immunosorbent assay antibody test results from long-term care facilities and skilled nursing staff in Colorado between May and December of 2020.ResultsWe found the extreme value approach had minimal bias when targeting a specificity of 0.995. Using the empirical quantile of the negative controls performed well when targeting a specificity of 0.95. The higher target specificity is preferred for overall test accuracy when prevalence is low, whereas the lower target specificity is preferred when prevalence is higher and resulted in less variable prevalence estimation.DiscussionWhile commonly used, the normal based methods showed considerable bias compared to the empirical and extreme value theory-based methods.ConclusionsWhen determining disease testing cutoffs from small training data samples, we recommend using the extreme value based-methods when targeting a high specificity and the empirical quantile when targeting a lower specificity.

Interest rate risk of Chinese commercial banks based on the GARCH-EVT model

Interest rate market risk faced by China’s commercial banks is increasing after the announcement that the interest rate marketisation is completed. This paper examines the Value-at-Risk, and statistical properties in the daily price return of Shanghai banks’ overnight offered rate. The study applies two-stage approaches, combining GARCH-type models with extreme value theory. Firstly, the Markov regime switching model is used to test the regime states of the series. Secondly, the performance of different VaR models are examined. Results show that the extreme value approach estimates better at the 99% confidence level. The EGARCH-GED model is the most suitable of the employed GARCH-type models. The back-testing results support the idea that the approach used in this study is appropriate for improving commercial banks’ daily risk management. This paper applies the GARCH-EVT method for interest rate measurement after China’s interest rate marketisation and added regime analysis of interest rate. Suggested policy implications will help formulate policies that guide the activities of commercial banks in China.

Determining return levels of extreme daily precipitation, reservoir inflow, and dry spells

Return level calculations are widely used to determine the risks that extreme events may pose to infrastructure, including hydropower site operations. Extreme events (e.g., extreme precipitation and droughts) are expected to increase in frequency and intensity in the future, but not necessarily in a homogenous way across regions. This makes localized assessment important for understanding risk changes to specific sites. However, for sites with relatively small datasets, selecting an applicable method for return level calculations is not straightforward. This study focuses on the application of traditional univariate extreme value approaches (Generalized Extreme Value and Generalized Pareto) as well as two more recent approaches (extended Generalized Pareto and Metastatistical Extreme Value distributions), that are specifically suited for application to small datasets. These methods are used to calculate return levels of extreme precipitation at six Alpine stations and high reservoir inflow events for a hydropower reservoir. In addition, return levels of meteorological drought and low inflow periods (dry spells) are determined using a non-parametric approach. Return levels for return periods of 10- and 20- years were calculated using 10-, 20-, and 40- years of data for each method. The results show that even shorter timeseries can give similar return levels as longer timeseries for most methods. However, the GEV has greater sensitivity to sparse data and tended to give lower estimates for precipitation return levels. The MEV is only to be preferred over GPD if the underlying distribution fits the data well. The result is used to assemble a profile of 10- and 20-year return levels estimated with various statistical approaches, for extreme high precipitation/inflow and low precipitation/inflow events. The findings of the study may be helpful to researchers and practitioners alike in deciding which statistical approach to use to assess local extreme precipitation and inflow risks to individual reservoirs.

Estimating real-time crash risk at signalized intersections: A Bayesian Generalized Extreme Value approach

The current reactive road safety assessment cannot assess real-time crash risk at signalized intersections, and as such, the real-time risk mitigation strategies could not be developed. This shortcoming is mainly attributed to a lack of a proper methodological framework that could reveal insights into the real-time crash risk using the crash signatures or precursor of crashes, otherwise known as traffic conflicts, near misses, or surrogate safety measures. This study proposes a traffic conflict-based crash estimation technique to estimate real-time crash risk at signalized intersections. In particular, a Bayesian modeling framework is employed to estimate crash risk in real-time from traffic conflicts identified by modified time-to-collision (MTTC). A Block Maxima approach corresponding to generalized extreme value distribution is used to identify traffic extremes at a micro (i.e., traffic signal cycle) level. Then, the traffic flow at the signal cycle level is included as a covariate in the model to explain time-varying crash risk across different cycles. The unobserved heterogeneity associated with the crash risk of different cycles is also addressed within the Bayesian framework. The proposed framework is tested using a total of 96 h of traffic movement video data from a signalized intersection in Queensland, Australia. A comparison between the estimated crashes and the historical crash records demonstrates the suitability of the developed model for crash risk estimations. The crash risk of each signal cycle is identified by generating a different generalized extreme value distribution for each traffic signal cycle. Further statistical analyses reveal that crash risk varies within the different periods of a typical day, with higher crash risks found during the morning and evening peak periods. This study concludes the efficacy of the proposed real-time framework in estimating the rear-end crash risk at the micro-level, allowing proactive safety management and the development of risk mitigation strategies.

Modelling maximum cyber incident losses of German organisations: an empirical study and modified extreme value distribution approach

Cyber incidents are among the most critical business risks for organisations and can lead to large financial losses. However, previous research on loss modelling is based on unassured data sources because the representativeness and completeness of op-risk databases cannot be assured. Moreover, there is a lack of modelling approaches that focus on the tail behaviour and adequately account for extreme losses. In this paper, we introduce a novel ‘tempered’ generalised extreme value (GEV) approach. Based on a stratified random sample of 5000 interviewed German organisations, we model different loss distributions and compare them to our empirical data using graphical analysis and goodness-of-fit tests. We differentiate various subsamples (industry, size, attack type, loss type) and find our modified GEV outperforms other distributions, such as the lognormal and Weibull distributions. Finally, we calculate losses for the German economy, present application examples, derive implications as well as discuss the comparison of loss estimates in the literature.

Improved Extreme Rainfall Frequency Analysis Using a Two‐Step Kappa Approach

AbstractAccurate estimation of annual exceedance probabilities (AEPs) of extreme rainfalls through rainfall frequency analysis is a critical step in engineering design for flood mitigation and disaster response. Here we show how the estimation of rainfall frequency curves can be improved by fitting a four‐parameter Kappa distribution to a peaks‐over‐threshold (POT) series. To fit the Kappa distribution to POT data we present a two‐step fitting approach based on maximum likelihood estimation which separately models storm intensity and the arrival frequency. First, a Generalized Pareto distribution (GPA) describing storm intensity is fitted, followed by a Binomial distribution for storm arrivals. We compare the performance of this two‐step Kappa approach to an analogous two‐step Generalized Extreme Value (GEV) approach and to Kappa and GEV distributions fitted to annual maxima series (AMS), using both synthetic and real‐world data representative of Australian climatic conditions. The experiments show that leveraging additional information from the POT series in the two‐step Kappa approach dramatically improves quantile estimation and reduces uncertainty compared to fitting either the GEV or the Kappa distributions to AMS, particularly for rare quantiles. When skew–kurtosis properties of extreme rainfalls are well represented by the Kappa but not the GEV, the two‐step Kappa approach yields unbiased quantiles under extrapolation, while the use of GEV can lead to highly biased estimates. From these results, we believe the two‐step Kappa approach is suitable for both at‐site and regional rainfall frequency analyses as it can accommodate distributions ranging from GPA to GEV without encountering over‐fitting problems generally associated with four‐parameter distributions.

Modeling the COVID-19 Travel Choices in Colombia and India: A Hybrid Multiple Discrete-Continuous Nested Extreme Value Approach.

The COVID-19 pandemic has affected many daily activities, primarily as a result of the perceived contagion risk and government restrictions to mitigate the spread of the virus. To this end, drastic changes in the trip choices for commuting to work have been reported and studied, mostly through descriptive analysis. On the other hand, modeling-based research that can simultaneously understand both changes in mode choice and its frequency at an individual level has not been much used in existing studies. As such, this study aims to understand the changes in mode-choice preference and the frequency of trips, comparing pre-COVID with during-COVID scenarios, in two different countries of the Global South: Colombia and India. A hybrid multiple discrete-continuous nested extreme value model was implemented using the data obtained from online surveys in Colombia and India during the early COVID-19 period of March and April 2020. This study found that, in both countries, utility related to active modes (more used) and public transportation (less used) changed during the pandemic. In addition, this study highlights potential risks in likely unsustainable futures where there may be increased use of private vehicles such as cars and motorcycles, in both countries. It was also identified that perceptions toward government responses had a significant impact on the choices in Colombia, though this was not the case in India. These results may help decision makers focus on public policies to encourage sustainable transportation by avoiding the detrimental long-term behavioral changes resulting from the COVID-19 pandemic.

Forecasting tail risk measures for financial time series: An extreme value approach with covariates

Forecasting tail risk measures for financial time series: An extreme value approach with covariates

Effect of vehicle size on crash risk in a heterogeneous traffic scenario: a bivariate extreme value approach

ABSTRACT Most traffic conflict indicators are defined for car-following scenarios where a follower vehicle interacts with a leader vehicle in one-dimensional space. However, vehicles do interact in a two-dimensional space especially in a heterogeneous traffic environment. Further, designating an interaction as risky depends on the interacting leader-follower (LF) pairs. Conflict indicators namely Time-to-Collision (TTC) and lateral gap which quantifies longitudinal and lateral interactions respectively, were computed from video recordings at four accident black spots on four-lane divided highways. Conflict in two-dimensional space was modelled for various LF-pairs using the Bivariate Extreme Value function of these two conflict indicators. Crash risk was estimated for each LF-pairs separately. Results show that cars and light commercial vehicles exhibit higher crash risk as compared to two-wheelers and motorized three-wheelers. The proposed framework can be used for more accurate risk assessment and calibration of collision warning systems in lane free mixed traffic conditions.

Probabilistic earthquake hazard parameterization for Indo-Burma region using extreme value approach

The Indo-Burma area is one of the most seismically active regions because of subduction of the Indian plate under the Burmese plate. The Indo-Burma area, which is bordered by 22°–27°N and 92°–97°E, has of late witnessed multiple moderate-to-large earthquakes. Seismic hazard assessment has been performed using the well-known extreme value theory, including estimate of return periods and likelihood of occurrence of medium to large earthquake events. The Indo-Burma region's seismic hazard parameterization has been computed using a homogeneous and thorough earthquake database created for the time span between 1973 and 2021. Due to an insufficient dataset, the b-value calculated using the GR relation was determined to be unsatisfactory (0.58). Therefore, the b-value was estimated using Gumbel's extreme value approach (0.902). The findings show that earthquake of 5.352 magnitude is likely to be the greatest annual earthquake in the study area. Additionally, the most likely large earthquakes that might happen throughout a wide range of periods have been projected and displayed.

Extreme weather events and high Colombian food prices: A non‐stationary extreme value approach1

AbstractGiven the importance of climate change and the increase of its severity under extreme weather events, we analyze the main drivers of high food prices in Colombia between 1985 and 2020 focusing on extreme weather shocks like a strong El Niño. We estimate a non‐stationary extreme value model for Colombian food prices. Our findings suggest that perishable foods are more exposed to extreme weather conditions in comparison to processed foods. In fact, an extremely low precipitation level explains only high prices in perishable foods. The risk of high perishable food prices is significantly larger for low rainfall levels (dry seasons) compared to high precipitation levels (rainy seasons). This risk gradually results in higher perishable food prices. It is nonlinear and is also significantly larger than the risk related to changes in the US dollar‐Colombian peso exchange rate and fuel prices. Those covariates also explain high prices for both perishable and processed foods. Finally, we find that the events associated with the strongest El Niño in 1988 and 2016 are expected to reoccur once every 50 years.

Multi-Hazard Assessment of a Flood Protection Levee

Earthquake-induced liquefaction is one of the main causes of levee breaches that can threaten human life and property. Conventionally, liquefaction hazard has been assessed in terms of the factor of safety FoS against liquefaction which ignores the potential variability of groundwater table (GWT) due to precipitation events. A probabilistic methodology, taking into account these GWT variations over time, is therefore presented in this study to assess the liquefaction hazard of an earthen flood protection levee. A frequency analysis based on the Annual Maxima/Generalised Extreme Value (AM/GEV) approach is first used to characterize the distribution of GWT extreme values. The CPT-based method is then applied with the provided GWT scenarios to predict liquefaction and display the hazard curves. Assuming a single constant GWT estimate during an earthquake revealed a certain liquefaction hazard within a sandy layer. Considering GWT variations during earthquakes showed, however, that liquefaction is unlikely to occur with an FoS threshold set at 1.0. These findings highlight: (1) the conservatism of the conventional approach that overestimates the liquefaction hazard, (2) the importance of the proposed probabilistic approach as a complementary tool for more reliable decision-making, and (3) the dependency of liquefaction hazard predictions on the degree of uncertainty in GWT estimates and FoS threshold.

Climatic and altitudinal controls on rainfall extremes and their temporal changes in data-sparse tropical regions

• We used the Simplified MEV to model extreme rainfall quantiles in tropical regions. • Weibull distribution well approximates the tail of daily rainfall distribution. • Statistical parameters and rainfall quantiles significantly depend on latitude. • Homogeneous patterns in regional temporal trends are related to altitude. • Extreme daily rainfall amounts in the Volta basin increased during 1978–2018. Sub-Saharan Africa’s economy and livelihood are primarily dependent on agriculture, which makes it highly vulnerable to the impacts of extreme weather events and climate change. Modelling and quantifying extreme rainfall and its temporal changes in such environments could thus provide crucial information for design, insurance, management, ecology and climate adaptation. Rain gauge networks in the area are relatively sparse, and often characterized by missing data, which hamper the use of extreme-value methods for estimating extreme precipitation quantiles. In this study, we adopted the Simplified Metastatistical Extreme Value approach for the estimation of extreme return levels based on ordinary events (i.e., all the independent realizations of the variable of interest), which was shown to be more accurate than traditional extreme-value methods in the presence of short data records. We examined data from 66 rain gauges covering diverse hydro-climatic regions across Ghana with the aim of (i) validating the robustness of the statistical approach, (ii) characterising the climatic and altitudinal controls on the occurrence, frequency and intensity of rainfall extremes, and (iii) quantifying recent changes in the characteristics of extremes. We found that a two-parameter Weibull distribution well approximates the tail of the daily rainfall distribution throughout the area. Our statistical approach can quantify extremes with largely reduced uncertainties (7–17% uncertainty in the 100-year return levels computed using 10 years of data versus 11–62% of extreme-value based methods). Extreme precipitation statistics (daily intensity distribution, number of wet days, extreme rainfall quantiles) are found to significantly depend on latitude, so that the four latitudinally layered hydro-climatic regions typically adopted in the area well represent spatial variations. Elevation significantly affects the tail heaviness of the daily intensity distribution and thus extreme rainfall quantiles. Temporal changes during the period 1978–2018 are found to be non-homogeneous in the area as well as within the four hydro-climatic regions, but are homogeneous in three altitude-based regions. We report contrasting trends in extreme return levels in low-elevation (<200 m a.s.l.) and hilly regions, related to contrasting changes in the daily intensity distribution. Statistically significant positive trends in extreme daily rainfall amounts are observed in the inland low-elevation region of the Volta river basin, which call for further investigation of changes in future precipitation extremes in this extremely important hydrological region in Sub-Saharan Africa.

A non-stationary extreme-value approach for climate projection ensembles: application to snow loads in the French Alps

Abstract. Anticipating risks related to climate extremes often relies on the quantification of large return levels (values exceeded with small probability) from climate projection ensembles. Current approaches based on multi-model ensembles (MMEs) usually estimate return levels separately for each climate simulation of the MME. In contrast, using MME obtained with different combinations of general circulation model (GCM) and regional climate model (RCM), our approach estimates return levels together from the past observations and all GCM–RCM pairs, considering both historical and future periods. The proposed methodology seeks to provide estimates of projected return levels accounting for the variability of individual GCM–RCM trajectories, with a robust quantification of uncertainties. To this aim, we introduce a flexible non-stationary generalized extreme value (GEV) distribution that includes (i) piecewise linear functions to model the changes in the three GEV parameters and (ii) adjustment coefficients for the location and scale parameters to adjust the GEV distributions of the GCM–RCM pairs with respect to the GEV distribution of the past observations. Our application focuses on snow load at 1500 m elevation for the 23 massifs of the French Alps. Annual maxima are available for 20 adjusted GCM–RCM pairs from the EURO-CORDEX experiment under the scenario Representative Concentration Pathway (RCP) 8.5. Our results show with a model-as-truth experiment that at least two linear pieces should be considered for the piecewise linear functions. We also show, with a split-sample experiment, that eight massifs should consider adjustment coefficients. These two experiments help us select the GEV parameterizations for each massif. Finally, using these selected parameterizations, we find that the 50-year return level of snow load is projected to decrease in all massifs by −2.9 kN m−2 (−50 %) on average between 1986–2005 and 2080–2099 at 1500 m elevation and RCP8.5. This paper extends the recent idea to constrain climate projection ensembles using past observations to climate extremes.

Investigation of Shifts in Time Use Behavior during the COVID-19 Pandemic: A Mixed Multiple Discrete-Continuous Extreme Value Approach with Panel GPS Data

Typical patterns of time use and travel behavior have been transformed by the COVID-19 pandemic. The drastic change has been documented in several studies to date, especially in the realm of transport, which have asked respondents about how their behavior has changed compared with their prepandemic routines. This work complements those efforts, offering a valuable evaluation of the decision-making process behind choosing which activities to engage in and for how long. A mixed multiple discrete-continuous extreme value (MMDCEV) model was applied to panel GPS data collected between September 2019 and October 2020. The estimation results uncovered how different demographic and mobility tool ownership characteristics affected the choice of activities and their duration. Additional interaction effects of different time periods exogenously introduced into the model allowed for the assessment of the differential effects of these components. Our findings revealed that the choice to participate in out-of-home activities strongly differed with respect to prepandemic conditions. Not only were individuals choosing to spend more time at home during the pandemic, but when they did engage in out-of-home activities, it was also for a shorter duration. Notably, age, gender, education level, and income all affected the propensity to engage in out-of-home activities during the pandemic. These results and their implications for policy as we try to plan for the “new normal” daily life are discussed.

Investigation of multiple-presence factor for traffic loads on road-rail bridges based on a novel extreme value analysis approach

Multiple-presence factor (MPF) is an efficient measure for calculating traffic load effects on bridges with multiple lanes. It takes into account the probability of multiple heavy vehicles that simultaneously present in adjacent lanes. Though road-rail bridges carrying both road and rail traffic are common in modern cities, no sophisticated method is available to obtain the MPFs for the combined traffic loads. This study presents a novel extreme value analysis approach to predict the extreme load effects on road-rail bridges and investigate the corresponding MPFs. The core of the new approach is an unsupervised clustering algorithm based on a generalized extreme value mixture model (GEVMM), which can fit data with mixed distribution characteristics and can predict extreme values. The road-vehicle flow is represented by vehicle parameters and traffic parameters. The train flow is generated based on the distribution of passenger volume and train schedule. The 1000-day load effects on road-rail bridges with various spans are simulated and then used to predict the maximum load effects in 100 years based on the proposed method and the conventional generalized extreme value (GEV) approach, respectively. The comparison among the predicted maximum load effects and those obtained from the simulated 100-year road-rail traffic flow shows that the proposed approach is more reliable than the conventional GEV approach. Then the MPF values of the road-rail bridges are calculated from the predicted maximum load effects during a specified return period of 2000 years. The proposed method provides a valuable reference for the design and evaluation of road-rail bridges with various spans.