Extreme Value Model Research Articles

The most massive Population III stars

ABSTRACT Recent data from the JWST suggest that there are realistic prospects for detecting the earliest generation of stars at redshift ∼20. These metal-poor, gaseous Population III (Pop III) stars are likely in the mass range $10\!-\!10^3\, {\rm M}_{\odot }$ . We develop a framework for calculating the abundances of Pop III stars as well as the distribution of the most massive Pop III stars based on an application of extreme-value statistics. Our calculations use the star formation rate density from a recent simulation to calibrate the star formation efficiency from which the Pop III stellar abundances are derived. Our extreme-value modelling suggests that the most massive Pop III stars at redshifts 10 < z < 20 are likely to be $\gtrsim 10^3\!-\!10^4\, {\rm M}_\odot$ . Such extreme Pop III stars were sufficiently numerous to be the seeds of supermassive black holes at high redshifts and possibly source detectable gravitational waves. We conclude that the extreme-value formalism provides an effective way to constrain the stellar initial mass function.

Temperature gradient zoning of steel beams without paving layers in China

The solar temperature field and its temperature effects on the straddle monorail tourist transportation system (SMTTS) significantly affect its mechanical performance. To investigate the distribution law of the daylight temperature field of the unpaved steel beams, the daylight temperature fields of box-type and I-sectional steel beams in different regions were measured and simulated. With the simulation results, the vertical temperature gradient curves of the unpaved steel girders were determined. Afterward, with the historical meteorological data as variables, the parameters of the extreme value model of generalized extreme value (GEV) distribution were obtained, and the representative values of temperature differences in China, based on the recurrence period, were analyzed. By analyzing the temperature difference values in 34 cities in China, an empirical prediction formula for the representative temperature difference value with three parameters was proposed, and the temperature gradient partition was established. The results indicated that the vertical temperature gradients of closed-section steel box girders are about 2–3 °C greater than that of open-section I-beams. Moreover, there are apparent geographical differences in the temperature difference values of steel girders.

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.

Projected changes in extreme streamflow and inland flooding in the mid-21st century over Northeastern United States using ensemble WRF-Hydro simulations

Study regionNortheastern United States (NEUS). Study focusWe investigate the potential impacts of climate change on precipitation, streamflow, and inland flooding in the NEUS during the mid-21st century. Dynamically downscaled climate projections from three global climate models for historical (1995–2004) and future (2045–2054) periods under business-as-usual scenarios were used to force the hydrologic model WRF-Hydro at 200-meter resolution and create ensemble hydrologic simulations. Additionally, an extreme value model was developed to project the risks associated with low-frequency hydrologic events. New hydrological insights for the regionResults from four major watersheds indicate a significantly wetter regime in winter months and potential drier conditions during late spring to early summer. Discharges in fall are projected to decrease in the northern watersheds and increase toward the south. Extreme flow and water depths resulting from extreme inland flooding are projected to increase by 5–20% and > 100%, respectively. The extent of the total flooded area is likely to be 20% greater by the mid-century. These increased risks can be attributed to (i) an approximate 25% increase in decadal mean and > 40% increase in decadal extreme precipitation intensity, (ii) up to 30% lower snow availability and 5–25% higher evapotranspiration throughout the year, and (iii) a projected 5% increase in soil moisture in all seasons except summer. Furthermore, rapid snow melting in winter will likely cause an earlier peak flow in the rivers.

Extreme value modelling of SARS-CoV-2 community transmission using discrete generalized Pareto distributions.

Superspreading has been suggested to be a major driver of overall transmission in the case of SARS-CoV-2. It is, therefore, important to statistically investigate the tail features of superspreading events (SSEs) to better understand virus propagation and control. Our extreme value analysis of different sources of secondary case data indicates that case numbers of SSEs associated with SARS-CoV-2 may be fat-tailed, although substantially less so than predicted recently in the literature, but also less important relative to SSEs associated with SARS-CoV. The results caution against pooling data from both coronaviruses. This could provide policy- and decision-makers with a more reliable assessment of the tail exposure to SARS-CoV-2 contamination. Going further, we consider the broader problem of large community transmission. We study the tail behaviour of SARS-CoV-2 cluster cases documented both in official reports and in the media. Our results suggest that the observed cluster sizes have been fat-tailed in the vast majority of surveyed countries. We also give estimates and confidence intervals of the extreme potential risk for those countries. A key component of our methodology is up-to-date discrete generalized Pareto models which allow for maximum likelihood-based inference of data with a high degree of discreteness.

Chinese Technical Guideline for Deriving Water Quality Criteria for Protection of Freshwater Organisms

In recent years, China has determined the national goal of "developing national environmental criteria", thereby promoting the rapid development of environmental quality criteria research in China. In 2017, the Ministry of Ecology and Environment of China (MEEC, formerly the Ministry of Environmental Protection of China) issued the technical guideline for deriving water quality criteria (WQC) for protection of freshwater organisms (HJ 831-2017), and in 2022, they organized the guideline revision and issued an updated version (HJ 831-2022). The primary contents of the revision included the following. The minimum toxicity data requirements were upgraded from 6 to 10, and the species mean toxicity value was replaced by the same effect toxicity value for the criteria calculation. It is now required that the tested organisms must be distributed in China's natural fresh waters, and the toxicity data of non-native model species will no longer be used. The list of freshwater invasive species in China that cannot be used as test species was added into the guideline. The acute/chronic ratio (ACR) method for the criteria derivation and the extreme value model were deleted, and the provisions for testing the toxicity data distribution were also deleted. The exposure time of the toxicity test of various tested organisms was refined, and the priority of the toxicity data was clearly specified. This paper introduces the framework and specific technical requirements of HJ 831-2022 in detail, including data collection, pre-processing of toxicity data, criteria derivation, fitting models, and quality control. This introduction is helpful for international peers to understand the latest research progress of China's WQC.

New estimation methods for extremal bivariate return curves

AbstractIn the multivariate setting, estimates of extremal risk measures are important in many contexts, such as environmental planning and structural engineering. In this paper, we propose new estimation methods for extremal bivariate return curves, a risk measure that is the natural bivariate extension to a return level. Unlike several existing techniques, our estimates are based on bivariate extreme value models that can capture both key forms of extremal dependence. We devise tools for validating return curve estimates, as well as representing their uncertainty, and compare a selection of curve estimation techniques through simulation studies. We apply the methodology to two metocean data sets, with diagnostics indicating generally good performance.

The importance of context in extreme value analysis with application to extreme temperatures in the U.S. and Greenland

Abstract Statistical extreme value models allow estimation of the frequency, magnitude, and spatio-temporal extent of extreme temperature events in the presence of climate change. Unfortunately, the assumptions of many standard methods are not valid for complex environmental data sets, with a realistic statistical model requiring appropriate incorporation of scientific context. We examine two case studies in which the application of routine extreme value methods result in inappropriate models and inaccurate predictions. In the first scenario, incorporating random effects reflects shifts in unobserved climatic drivers that led to record-breaking US temperatures in 2021, permitting greater accuracy in return period prediction. In scenario two, a Gaussian mixture model fit to ice surface temperatures in Greenland improves fit and predictive abilities, especially in the poorly-defined upper tail around 0∘C.

Smooth copula‐based generalized extreme value model and spatial interpolation for extreme rainfall in Central Eastern Canada

AbstractThis paper proposes a smooth copula‐based Generalized Extreme Value (GEV) model to map and predict extreme rainfall in Central Eastern Canada. The considered data contains a large portion of missing values, and one observes several nonconcomitant record periods at different stations. The proposed two‐step approach combines GEV parameters' smooth functions in space through the use of spatial covariates and a flexible hierarchical copula‐based model to take into account dependence between the recording stations. The hierarchical copula structure is detected via a clustering algorithm implemented with an adapted version of the copula‐based dissimilarity measure recently introduced in the literature. Finally, we compare the classical GEV parameter interpolation approaches with the proposed smooth copula‐based GEV modeling approach.

An efficient Bayesian modelling of extreme winds in the favour​ of energy generation in Pakistan

Daily and annual maximum wind speed quantiles can be estimated using extreme value theory for any metrological site of interest. These estimates are of vast importance for modelling and predicting maximum wind speed. This paper develops an efficient modelling paradigm of extreme winds by analysing daily and annual maximum wind speed data via frequentist and Bayesian methodologies. For this purpose, the generalized extreme value (GEV) model is used for yearly maxima, and the generalized Pareto distribution (GPD) is used for daily exceedance over a high threshold. In frequentist inference, the parameters of both models are estimated using the maximum likelihood and linear moments method. In contrast, the Bayesian Markov Chain Monte Carlo procedure with the Metropolis–Hasting algorithm is used. In addition, the informative priors for both models are constructed empirically using historical records of wind speed data from five other weather stations of Pakistan and one belonging to India. The results show that the Bayesian modelling provides apparent benefits in terms of improved accuracy in the estimation of the parameters as well as return levels of both distributions. Furthermore, the Bayesian analysis expresses that posterior inference might be affected by the choice of priors used to formulate the informative priors. Overall, based on assessment measures, the GPD fitted through Bayesian informative priors provides an efficient estimation strategy in terms of precision than other frameworks when uncertainty in parameters and return levels are taken into account. Our methodology can be implemented easily to other regions by considering the prior information from the border area stations of other countries (e.g., China, Afghanistan, India, and Iran). Moreover, the return level estimates of the GPD based on informative Bayesian priors are very beneficial in policymaking and wind energy generation engineering for the Thatta region of the country.

Estimation of associated values from conditional extreme value models

The design and reanalysis of offshore and coastal structures usually requires the estimation of return values for dominant metocean variables (such as significant wave height) and associated values for other variables (such as peak spectral period or wind speed) from a finite sample of data; these are typically estimated using extreme value analysis. Yet the parameters of extreme value models can only be estimated with error from finite data. Different choices available to summarise uncertain information about the characteristics of the tail of a multivariate distribution in a small number of summary statistics (such as return values and associated values) complicates their estimation, especially for small sample sizes: choices regarding the ordering of mathematical operations lead to estimators of return values and associated values with different finite sample bias and variance characteristics. The current work extends a previous study (Jonathan et al.,2021) into the performance of estimators for marginal return values in the presence of sampling uncertainty, to estimators of associated values based on the bivariate conditional extremes model (Heffernan and Tawn, 2004) and competitors. Using a large designed simulation experiment, we explore the performance of combinations of 12 different estimators and three bivariate model candidates. The rich set of results from the simulation experiment are reported and explained in detail. Briefly: (a) calculation of associated values is only always feasible from small samples using two of the 12 estimators, which should be preferred; (b) estimators exploiting the median rather than the mean to summarise a distribution are more robust, and should also be preferred, especially for small sample sizes; (c) extreme value models incorporating appropriate descriptions of marginal and dependence provide better estimation of associated values for larger sample size; and (d) summarising the joint tail of metocean variables (in terms of return values and associated values) should be avoided where possible, in favour of probabilistic risk analysis of structural failure incorporating full uncertainty propagation.

Intensity-duration-frequency curves in the Guangdong-Hong Kong-Macao Greater Bay Area inferred from the Bayesian hierarchical model

Study regionThe Guangdong-Hong Kong-Macao Greater Bay Area (GBA), China. Study focusUsing hourly rain gauge data and CMORPH data, we use the duration-dependent generalized extreme value (d-GEV) model and the scaling invariant GEV model inferred by the Bayesian hierarchical model to derive the intensity-duration-frequency IDF characteristics of extreme precipitation in GBA and adjust their uncertainties. New hydrological insights for the regionThe GEV location and scale parameters of IDF curves in GBA show similar spatial distribution and the higher-resolution CMORPH can capture more local details than rain gauge data. Meanwhile, compared with the rain gauge data, CMORPH produces significantly lower rainfall intensity of storms with short durations, which leads to large uncertainties of IDF curves derived from CMORPH for the short-duration rainfall. Additionally, the uncertainties of IDF curves can be substantially reduced by using the scaling invariant model that was inferred by the Bayesian hierarchical model, compared with the ordinary d-GEV method. Therefore, the Bayesian inference is suggested to be adopted for regional estimation of IDF curves, especially for regions of limited sub-daily gauge data.

A conflict-based safety assessment technique for rear-end crash risk at signalized intersections in a lower-middle-income country: A comparison between homogeneous and heterogeneous traffic conditions

Rear-end crashes at signalized intersections are attributed to different traffic behavior and operational characteristics. However, the influences of homogenous traffic conditions in developed countries and heterogeneous traffic conditions in low and middle-income developing countries like India are rarely explored. This study aims to examine the spatial–temporal characteristics of rear-end crash risk at signalized intersections characterized by lane-disciplined homogeneous and non-lane-based heterogeneous traffic conditions. In particular, this study has applied a conflict-based safety assessment framework to compare the rear-end crash risks across these traffic conditions. Vehicular trajectory data of vehicles at four signalized intersections, one in the homogeneous and three in heterogeneous traffic conditions, is analyzed. Rear-end conflicts position and time of occurrence in the upstream and downstream section of the stop-line are identified and modeled by extreme value models. Results show that the vehicles in heterogeneous traffic conditions are more aggressive, resulting in a higher number of conflicts and probable crashes. The presence of smaller-sized vehicles in dominating proportions and disregard of lane discipline with a higher degree of lateral movement are responsible for more traffic conflicts. The estimated extreme value models suggest that the minimum rear-end crash risk probability at signalized intersections with heterogeneous traffic conditions is about three times higher than that at signalized intersections with homogeneous traffic conditions. The observation is similar for crash risks estimated from both surrogate safety measures used in this study. The weak lane discipline and irregular lateral movement of vehicles are responsible for higher crash risks in heterogeneous traffic conditions.

Joint estimation of extreme spatially aggregated precipitation at different scales through mixture modelling

Although most models for rainfall extremes focus on pointwise values, it is aggregated precipitation over areas up to river catchment scale that is of the most interest. To capture the joint behaviour of precipitation aggregates evaluated at different spatial scales, parsimonious and effective models must be built with knowledge of the underlying spatial process. Precipitation is driven by a mixture of processes acting at different scales and intensities, e.g., convective and frontal, with extremes of aggregates for typical catchment sizes arising from extremes of only one of these processes, rather than a combination of them. High-intensity convective events cause extreme spatial aggregates at small scales but the contribution of lower-intensity large-scale fronts is likely to increase as the area aggregated increases. Thus, to capture small to large scale spatial aggregates within a single approach requires a model that can accurately capture the extremal properties of both convective and frontal events. Previous extreme value methods have ignored this mixture structure; we propose a spatial extreme value model which is a mixture of two components with different marginal and dependence models that are able to capture the extremal behaviour of convective and frontal rainfall and more faithfully reproduces spatial aggregates for a wide range of scales. Modelling extremes of the frontal component raises new challenges due to it exhibiting strong long-range extremal spatial dependence. Our modelling approach is applied to fine-scale, high-dimensional, gridded precipitation data. We show that accounting for the mixture structure improves the joint inference on extremes of spatial aggregates over regions of different sizes.

A general framework to obtain seamless seasonal–directional extreme individual wave heights—Showcase Ekofisk

Extreme wave climate provides the basis for safe design of offshore structures and is crucial for planning and executing offshore operations. Covariate modeling of extremes significantly enriches and improves estimates of return levels and exceedance probabilities of extreme sea states. Based on novel observational and hindcast datasets, we formulate a seasonal–directional extreme value model for individual wave heights and present exceedance probabilities for the Ekofisk oil and gas field, a location in the Central North Sea. Subsequently, we elucidate how to downscale estimates of monthly exceedance probabilities and return levels to daily maxima and illustrate how to retrieve consistent results on seamless directional sectors and different seasons, or for the entire covariate space. We conclude with a versatile statistical framework to obtain seasonal–directional extreme waves and reveal a strong seasonal and directional dependence of extreme individual waves at Ekofisk with the highest waves coming from northwest during winter. Moreover, we apply our approach to normalized wave heights and show noticeable variability depending on season and direction with implications for offshore design.

Extreme value modelling using the peaks over threshold method, an inverse cumulative uniform distribution approach

Extreme value modelling using the peaks over threshold method, an inverse cumulative uniform distribution approach

Extreme Value Analysis and Modelling of Wet Snow Accretion on Overhead Lines in Hungary

Wet snow events in Hungary can occasionally cause damage to overhead power lines and serious power supply failures. Return period calculation of such high snow mass events was determined upon a 50-year long data series available at 12 meteorological stations. Wet snow masses were estimated with a model of cylindrical accretion around wire of 3.1 cm diameter. Trends in the return periods and ice classes (according to the ISO 12494 standard) were assessed from division of the dataset into two periods (1965–1990 and 1991–2016). Ice classes in the range of R2 to R5 (mass of 0.7–6.1 kg m−1) were identified. The wet snow risk decreased in southern or central Hungary, while an increase was found in the western part of Hungary. Ice classes R6–R8 (up to 40 kg m−1) could occur in mountain areas of Hungary as indicated by numerical simulations in case studies. However, their return period is unknown due to the lack of long observation series.

Leading pedestrian intervals – Yay or Nay? A Before-After evaluation of multiple conflict types using an enhanced Non-Stationary framework integrating quantile regression into Bayesian hierarchical extreme value analysis

A pedestrian was estimated to be killed every 85 min and injured every 7 min on US roads in 2019. Targeted safety treatments are particularly required at urban intersections where pedestrians regularly conflict with turning vehicles. Leading Pedestrian Intervals (LPIs) are an innovative, low-cost treatment where the pedestrian and vehicle usage of the potential conflict area (a crosswalk) is staggered in time to give the pedestrians a head start of a few seconds and reduce the “element of surprise” for right-turning vehicles. The effectiveness of LPI treatment on pedestrian safety is mixed, and most importantly, its effect on vehicle-vehicle conflicts is unknown. This study investigates the before-after effects of LPI treatments on vehicle–pedestrian and vehicle-vehicle crash risk by applying traffic conflict techniques. In particular, this study has developed a quantile regression technique within the extreme value model to estimate and compare crash risks before and after the installation of the LPI treatment. The before-after traffic movement video data (504 h in total) were collected from three signalized intersections in the City of Bellevue, Washington. The recorded movements were analyzed using Microsoft’s proprietary computer vision platform, Edge Video Service, and Advanced Mobility Analytics Group’s cloud-based SMART SafetyTM platform to automatedly extract traffic conflicts by analyzing road user trajectories. The treatment effect was measured using a Bayesian hierarchical extreme value model with the peak-over threshold approach. For the extreme value model, a Bayesian quantile regression analysis was conducted to estimate the conflict thresholds corresponding to a high (95th) quantile. Odds ratios were estimated for both conflict types using untreated crossing as a control group. Results indicate that the LPI treatment reduces the crash risk of pedestrians as measured by the reduction in extreme vehicle–pedestrian conflicts by about 42%. The LPI treatment has also been found not to negatively affect rear-end conflicts along the approaches leading to the LPI-treated pedestrian crossing at the signalized intersections. The findings of this study further emphasize the effectiveness of video analytics in proactive safety evaluations of engineering treatments.

Adaptive surrogate model coupled with stochastic configuration network strategies for time-dependent reliability assessment

Time-dependent reliability assessment is crucial in enhancing product development economics and product performance sustainability throughout the lifecycle. It is still a challenge to accurately and efficiently evaluate the time-dependent reliability of engineering systems. This paper proposes a novel adaptive surrogate model method combining stochastic configuration network (SCN) and Kriging strategies to evaluate time-dependent reliability. SCN has accurate approximation ability and learning efficiency for strongly nonlinear systems that can overcome the conventional time-dependent reliability calculation, which is time-consuming and characterized by low accuracy. The proposed method first applies SCN to establish the response model of the performance function with respect to time and obtain the extreme value of the performance function. Then, Kriging is used to establish the extreme value model of the performance function with respect to the random variables based on the extreme value of performance function. The adaptive process considering the characteristics of random variables samples is adopted to update the extreme value model until the model meets the confidence target. Lastly, Monte Carlo simulation is employed for time-dependent reliability assessment based on the established extreme value model. Three example studies are used to demonstrate the effectiveness of the proposed approach for time-dependent reliability assessment.

A Bayesian generalised extreme value model to estimate real-time pedestrian crash risks at signalised intersections using artificial intelligence-based video analytics

Pedestrians represent a vulnerable road user group at signalised intersections. As such, properly estimating pedestrian crash risk at discrete short intervals is important for real-time safety management. This study proposes a novel real-time vehicle-pedestrian crash risk modelling framework for signalised intersections. At the core of this framework, a Bayesian Generalised Extreme Value modelling approach is employed to estimate crash risk in real-time from traffic conflicts captured by post encroachment time. A Block Maxima sampling approach, corresponding to a Generalised Extreme Value distribution, is used to identify pedestrian conflicts at the traffic signal cycle level. Several signal-level covariates are used to capture the time-varying heterogeneity of traffic extremes, and the crash risk of different signal cycles is also addressed within the Bayesian framework. The proposed framework is operationalised using a total of 144 hours of traffic movement video data from three signalised intersections in Queensland, Australia. To obtain signal cycle-level covariates, an automated covariate extraction algorithm is used that fuses three data sources (trajectory database from the video feed, traffic conflict database, and signal timing database) to obtain various covariates to explain time-varying crash risk across different cycles. Results show that the model provides a reasonable estimate of historical crash records at the study sites. Utilising the fitted generalised extreme value distribution, the proposed model provides real-time crash estimates at a signal cycle level and can differentiate between safe and risky signal cycles. The real-time crash risk model also helps understand the differential crash risk of pedestrians at a signalised intersection across different periods of the day. The findings of this study demonstrate the potential for the proposed real-time framework in estimating the vehicle-pedestrian crash risk at the signal cycle level, allowing proactive safety management and the development of real-time risk mitigation strategies for pedestrians.