Extreme Value Model Research Articles

Spatiotemporal patterns in precipitation whiplash over China during 1901–2100 based on CMIP6 simulations

Abstract The increasing risk of precipitation whiplash, characterized by rapid transitions between extreme drought and wet conditions, is largely related to atmospheric circulation changes due to anthropogenic greenhouse gas emissions. This study aims to examine the changing patterns of precipitation whiplash events for future projections (2021–2100) with regard to the current climate (1981–2020), and to unveil the relations between intensity, duration, and frequency of these events for various return periods across different regions of China. Multi-source observational datasets were also used to analyze the trend of precipitation whiplash indices for the current climate and to assess the ability of the CMIP6 ensemble model for reproducing the characteristics of precipitation whiplash events. The Intensity-Duration-Frequency (IDF) curves were estimated by using the nonstationary Generalized Extreme Value (GEV) model combined with Bayesian inference. The results show an increasing trend in frequency, intensity, and severity of precipitation whiplash events, particularly for the long-term future, while the duration of these transitions shows a decreasing trend. The peak occurrence months during the long-term future period exhibit notable changes in most parts of China. Specifically, the dry-to-wet whiplash events occur approximately two months earlier than in the current period, while the wet-to-dry whiplash occurs approximately two months later. The results also indicated that IDF curves shifted upward, particularly in the long-term future projections, suggesting an increased likelihood of more severe events. The findings of this study will serve as an essential reference for local authorities to develop more effective water resource management and disaster mitigation policies to tackle the impact of future climate change.

Topp-Leone generalization of the Generalized Pareto distribution and its impact on Extreme value modelling

Extreme Value theory (EVT) is a phenomenon used to model rare or extreme events and has been useful in well-known areas such as finance, economics, hydrology, insurance, etc. In this paper, we combine EVT and Bayesian statistics to estimate the extreme value index and other distribution parameters. EVT studies the behavior of the tails of the distribution, while Bayesian statistics allows us to incorporate prior knowledge of the parameters. The interdependence between these two statistical branches allows us to account for uncertainty in parameter and tail estimation. Block maxima and Peaks over Threshold are EVT divisions that are used to model observations. In this paper we use the Peaks over Threshold approach. The generalized Pareto distribution is a Peaks over Threshold distribution. Existing literature studied the generalizations and extensions of the generalized Pareto distribution. These extensions mostly focus on the positive domain of attraction. In this paper we contribute to the study of EVT by considering both the negative and positive domains of attraction. We consider the (Topp and Leone, 1955) generalization for the generalized Pareto distribution. We show, by means of a simulation study, that this distribution can effectively estimate the extreme value index and that it is less sensitive to threshold selection than the normal generalized Pareto distribution.

A Novel Reciprocal-Weibull Model for Extreme Reliability Data: Statistical Properties, Reliability Applications, Reliability PORT-VaR and Mean of Order P Risk Analysis

Peaks over a random threshold value-at-risk (PORT-VaR) analysis is a powerful tool for evaluating extreme value reliability data, particularly for materials like carbon and glass fibers. By incorporating random thresholds into traditional value at risk (VaR) and tail value at risk (TVaR) frameworks, it provides a more nuanced understanding of how materials behave under extreme conditions, making it invaluable for applications where failure is costly or dangerous, such as aerospace, automotive, and civil engineering. The combination of Mean of Order P (MO-P), VaR and PORT-VaR analyses in medical data offers important insights into risk evaluation and patient management. By examining both average and extreme strength of glass fibers, healthcare professionals can create more effective treatment plans, enhance patient outcomes, and improve overall care quality. This comprehensive approach enables more sophisticated decision-making and targeted interventions in clinical settings. To illustrate our main objective and conduct a medical analysis, we introduced a new extreme value model called the generalized Rayleigh reciprocal-Weibull (GR-RW) and presented its key mathematical results. Additionally, we conducted a simulation study and analyzed two real datasets to compare the competing models.

Individual preferences for food items within couples: Validating choice experiments predictions with real purchases data

AbstractDespite the popularity of choice experiments (CEs) for the valuation of environmental goods and services, some of its shortcomings have been only partially addressed by the literature. Among these, of particular saliency are the hypothetical nature of CEs and the lack of information on joint choices (e.g. choices made by couples) in traditional CEs. In this study, we contribute to filling these gaps by investigating joint choices concerning cheeses produced via different processes, involving environmental and social sustainability features. We use a two‐stage preference elicitation approach, using first stated and then real consumption choices collected from a sample of 90 couples. In the first stage, each member of the couples separately took part in a web survey with a hypothetical CE. In the second, these couples jointly engaged in a field experiment with monetary incentives in which they jointly chose the cheeses to purchase. This approach allows us to evaluate the role of individual preferences in shaping joint choices and to investigate whether predictions from stated choice data are congruent with, and validated by, real purchase data. We use CE data to estimate individual preferences with discrete choice models and use joint purchase data via the Multiple Discrete‐Continuous Nested Extreme Value model. Results suggest that joint real choices follow a substantively different decision process from that of individual stated choices.

SpatialGEV: Fast Bayesian inference for spatial extreme value models in R

SpatialGEV: Fast Bayesian inference for spatial extreme value models in R

Application of Machine Learning for Predictive Analysis and Management of Mediterranean-Farmed Fish Mortalities: A Risk Management Case Study Using Apache Spark

The current study evaluates the performance of three machine learning models—Decision Trees, Random Forest, and Linear Regression—applied to aquaculture data to mitigate risks in aquaculture management. The performances of these models are analyzed and properly demonstrated using metrics including the Mean Squared Error (MSE), R-squared (R2), Root Mean Squared Error (RMSE), and Concordance Index (C-index). The Random Forest model achieved the highest prediction accuracy among all machine learning models, followed by Linear Regression and the Decision Trees. The scatter plot for Linear Regression demonstrates good predictive accuracy for mid-range values. However, it shows significant deviations at the extremes, indicating that the model struggles to capture the full range of variability in the data. The bar chart of coefficients pinpoints the variables with the greatest impact on the predictions, providing suggestions for potential areas that can be improved and providing model interpretability. Future work could incorporate more predictive statistics models focusing on improving the models for extreme values by assessing non-linear models, feature engineering methods, and expanding research into less influential variables. The results greatly impact several sections, including aquaculture management, policy-making, and operational strategies, providing valuable insights for stakeholders and decision-makers. Apache Spark was used for data processing and machine learning model implementation; Apache Cassandra was also used for data storage, ensuring efficient large dataset management and SQL tools for structured data handling; Oracle VM VirtualBox for cross-platform virtualization; and Spark Connector was also used.

Spatial Extremal Modelling: A Case Study on the Interplay Between Margins and Dependence

ABSTRACTIt is no secret that statistical modelling often involves making simplifying assumptions when attempting to study complex stochastic phenomena. Spatial modelling of extreme values is no exception, with one of the most common such assumptions being stationarity in the marginal and/or dependence features. If non‐stationarity has been detected in the marginal distributions, it is tempting to try to model this while assuming stationarity in the dependence, without necessarily putting this latter assumption through thorough testing. However, margins and dependence are often intricately connected and the detection of non‐stationarity in one feature might affect the detection of non‐stationarity in the other. This work is an in‐depth case study of this interrelationship, with a particular focus on a spatio‐temporal environmental application exhibiting well‐documented marginal non‐stationarity. Specifically, we compare and contrast four different marginal detrending approaches in terms of our post‐detrending ability to detect temporal non‐stationarity in the spatial extremal dependence structure of a sea surface temperature dataset from the Red Sea.

Extreme-value modelling of migratory bird arrival dates: Insights from citizen science data

Abstract Citizen science mobilises many observers and gathers huge datasets but often without strict sampling protocols, resulting in observation biases due to heterogeneous sampling effort, which can lead to biased predictions. We develop a spatiotemporal Bayesian hierarchical model for bias-corrected estimation of arrival dates of the first migratory bird individuals at their breeding sites. Higher sampling effort could be correlated with earlier observed dates. We implement data fusion of two citizen-science datasets with fundamentally different protocols (BBS, eBird) and obtain posterior distributions of the latent process, which contains four spatial components endowed with Gaussian process priors: species niche; sampling effort; position and scale parameters of annual first arrival date. The data layer consists of four response variables: counts of observed eBird locations (Poisson); presence-absence at observed eBird locations (Binomial); BBS occurrence counts (Poisson); first arrival dates (Generalised Extreme-Value). We devise a Markov Chain Monte Carlo scheme and check by simulation that the latent process components are identifiable. We apply our model to several migratory bird species in the northeastern United States for 2001−2021 and find that the sampling effort significantly modulates the observed first arrival dates. We exploit this relationship to effectively bias-correct predictions of the true first arrivals.

Modelling household online shopping and home delivery demand using latent class & ordinal generalized extreme value (GEV) models

The surge in e-commerce during the past decade has led to dramatic changes in consumer shopping behaviour. The study applies two Generalized Extreme Value (GEV) family models to investigate households' e-shopping demands. The study proposes a model structure to jointly model ordinal-based choice behaviour with choice-makers' latent class membership. Introducing latent class structure with the OGEV formulation accounts for the relationship between choice-makers heterogeneous preferential groups and their ordinal choice outcomes. Furthermore, the study also applies the Ordered General Extreme Value (OGEV)-Negative Binomial (NB) model, capturing the interplay between consumers' in-store shopping demands and online shopping behaviour. The RUM principle inherited within the OGEV-NB model allows econometric valuation of in-store shopping activity explicitly considering households' e-shopping demands. Both models are empirically estimated using a dataset collected in the Greater Toronto Area (GTA), Canada. The empirical findings and behavioural implications are also discussed.

Overtaking risk assessment based on extreme value theory and intelligent network information

In order to evaluate the overtaking risk level of intelligent connected vehicles when providing different connected information, and to make up for the neglect of driver factors in traditional risk assessment and the inadequate evaluation of complex traffic scenarios by a single traffic conflict indicator, this paper introduces the Block maxima (BM) and Peak over threshold (POT) methods to fit the extreme value distribution for two conflict scenarios involved in overtaking events (following vehicle conflict and frontal vehicle conflict), so as to evaluate the risk of following vehicle accidents and frontal collision accidents during overtaking. In each conflict scenario, a non-stationary extreme value model considering driver factors and a binary extreme value model considering different traffic conflict indicators are constructed, and the model is verified by the overtaking test data of intelligent connected vehicles in a two-way two-lane vehicle. Overtaking events were extracted from the original test data and conflict indicators were calculated: including the collision time GAP with the front vehicle at the beginning of the overtaking event, the collision time TTC_t1 with the oncoming vehicle, the deceleration DRAC, and the collision time TTC with the oncoming vehicle and the headway time THW with the front vehicle at the end of the overtaking event. The probability of the event with a negative time conflict indicator or DRAC greater than MADR was used to characterize the degree of collision risk. The results show that in the following vehicle conflict scenario, the binary extreme value model constructed with different conflict indicators has different error results, among which the binary extreme value model constructed with THW&DRAC has the most accurate evaluation result (standard error MAE = 0.00028); in the front vehicle conflict scenario, the binary extreme value model constructed with TTC&DRAC has the most accurate evaluation result ( MAE = 0.006 ). In different conflict scenarios, the non- stationary extreme value model considering the driver factor significantly improves the risk assessment accuracy compared with the model without considering the driver factor (small AIC and BIC values). In addition, different intelligent network information (real-time distance, overtaking advice, speed advice) brings different overtaking risks, and when the intelligent network information is speed advice, the vehicle's overtaking risk is the lowest. Therefore, the non- stationary extreme value model and binary extreme value model considering driver factors proposed in this paper can effectively evaluate driving risks through traffic conflict indicators. Secondly, the experimental data of intelligent networked vehicles show that the extreme value theory model proposed in this paper can accurately evaluate the overtaking risk level of intelligent networked vehicles when providing different network information.

Modelling the complementarity and flexibility between different shared modes available in smart electric mobility hubs (eHUBS)

eHUBS are physical locations that integrate two or more electric shared mobility modes. As they provide transport users easier access to a wide range of transport modes, multimodal behaviour is expected to be more common. However, this issue has not been addressed in previous stated preference studies on mode choices involving innovative transport modes. In this study, multimodal behaviour is explicitly addressed both in measurement and in modelling by adopting the multiple discrete–continuous (MDC) modelling framework in contrast to discrete choice models. Instead of asking transport users to indicate the most preferred alternative, they were allowed to choose more than one alternative by allocating trips between several modes. This study aims to answer two questions: 1) whether there is complementarity between the multiple shared modes offered in eHUBS and 2) how would transport users adapt when one of the shared modes that they plan to use becomes unavailable. Using stated mode choice data of non-commuting trips from transport users whose current mode is driving a private car in Manchester, UK, several models under the MDC framework were estimated including Multiple Discrete-Continuous Extreme Value (MDCEV) model, mixed MDCEV model, and the extended Multiple Discrete Continuous (eMDC) model. The results show that there is complementarity between shared electric vehicle (EV) and electric bike (e-bike) offered in the eHUBS. In addition, the research show that the flexibility between those two shared modes is stronger than assumed in the MDCEV model, and common preference heterogeneity cannot fully account for this phenomenon.

Significance of different probability distributions in flood frequency analysis of Brahmani-Baitarani River Basin, India

Appropriate flood management in a basin requires analysis of peak discharge prediction and flood frequency. The main aim is to find the most suitable distribution model at various gauges for the entire Brahmani-Baitarani River basin for proper flood management. Daily flow data lengths ranging from 23 to 46 years for multiple gauges are obtained from the Central Water Commission. The present analysis employs the Generalized Extreme Value (GEV), Gumbel Max, Log-Pearson III (LP3), and Lognormal models to estimate the flood quantiles of various return periods. The L-moment, Method of Moment, and Maximum Likelihood Method are applied to estimate the model parameters. Goodness-of-fit tests, accuracy measures, and relative scoring indicated LP3 as the best-fit model, followed by GEV. The results indicated that floods with return periods of longer than 100 years can be considered for designing hydraulic structures in the upper reaches of the basin, whereas floods with return periods of longer than 50 years can be considered for the lower reaches. Significant constraints in the present study involve a limited number of gauges and their varied record lengths in this extensive basin. The findings of this study can be used in water resource planning, flood hazard mapping, and the design of hydraulic structures within similar catchments.

Flood risk and overtopping assessment for an exposed coastal road

The coastal village of Vík is located on the south coast of Iceland. The area is subjected to the full force of extratropical cyclones of the North Atlantic. The village beach is not a stable phenomenon; after a nearby volcanic eruption in 1918, it accreted by 500 m over 50 years but has eroded at similar rate since 1970, which poses increased flood risk in the area. There are plans to move the current ring road that lies through the village, with one possibility of it running along the coast. A study was conducted using multivariate extreme value modelling to determine the desired coastal defences needed for the new road. The method in question uses a multivariate joint probability model to simulate variables that cause coastal flooding events. It generates a large sample of extreme ocean events based on a 52-year time series of hindcast data. The large sample of extreme events was then used to determine return periods for overtopping events and to determine a desired crest height for coastal defence structures. The study puts forth suggestions of improvements on current coastal defence structures and the design specification for defence structures along a planned road along the coast.

Nudging consumers’ choices for niche milk: A real purchase experiment

Changing behaviours causing poor health is an ongoing global health challenge that requires developing adequate food policies and strengthening their effectiveness. Policies based on nudging have become increasingly popular internationally, but the literature provides mixed evidence of their effectiveness, with an intense academic debate. This study contributes to the debate by investigating the effect of different nudging techniques (availability enhancement, visibility enhancement and healthy eating calls) via a framed field experiment involving purchases of milk types. Participants were split into different nudging treatment groups and were endowed with a cash amount to purchase any desired quantity of the different products. We modelled observed choices via the multiple discrete–continuous nested extreme value model, which has yet to receive attention for the analysis of nudging effects on food choices. Results show that only the healthy eating call nudge effectively drove participants towards healthier milk choices, while the effect of other nudges is statistically insignificant. We provide simulated demand curves conditional on nudging treatments, which measure the effect of the latter on consumers’ consumption levels of the different milk types available.

Practical non-stationary extreme value analysis of peaks over threshold using the generalised Pareto distribution: Estimating uncertainties in return values

Choice of tuning parameters influences the performance of non-stationary extreme value modelling for peaks over threshold using the generalised Pareto (GP) distribution. We examine the effect of tuning parameter choice on maximum roughness-penalised likelihood estimation of GP models, the shape and scale parameters of which are assumed to vary smoothly on a one-dimensional “directional” covariate domain, under a B-spline representation. We examine the effect of (a) extreme value model parameterisation, (b) relative roughness penalty of GP parameters as a function of covariate, (c) cross-validation strategy for roughness parameter tuning, and (d) estimator for return value, on the estimation of return values corresponding to return periods 1000× the period of a sample of size 1000. Bootstrap resampling is used for thorough uncertainty quantification. We also compare results with those from stationary inference.Results from a large simulation study of 16 cases broadly representative of North Sea conditions for significant wave height with direction, indicate that (i) multiple two-group cross-validation yields lower return value estimates that ten-group cross-validation (leading to negative bias on average, for the case studies considered), (ii) the quantile of the bootstrap predictive estimator yields larger values than the mean over bootstraps of the quantile estimate (leading to reduced omni-directional bias for the case studies considered). Further, (iii) the use of stationary models for non-stationary tails is only reasonable when a high extreme value threshold is set for the stationary analysis. However, (iv) the relative performance of different modelling strategies is sensitive to the specific characteristics of the case study.

Inference with Extremes: Accounting for Extreme Values in Count Regression Models

Abstract Processes that occasionally, but not always, produce extreme values are notoriously difficult to model, as a small number of extreme observations may have a large impact on the results. Existing methods for handling extreme values are often arbitrary and leave researchers without guidance regarding this problem. In this paper, we propose an extreme value and zero-inflated negative binomial (EVZINB) regression model, which allows for separate modeling of extreme and nonextreme observations to solve this problem. The EVZINB model offers an elegant solution to modeling data with extreme values and allows researchers to draw additional inferences about both extreme and nonextreme observations. We illustrate the usefulness of the EVZINB model by replicating a study on the effects of the deployment of UN peacekeepers on one-sided violence against civilians.

Sample selection bias in non-traditional lending: A copula-based approach for imbalanced data

Credit scoring models for non-traditional lending channels, such as peer-to-peer (P2P) lending platforms, are usually estimated only on the sample of accepted applicants. This may lead to biased estimates of the risk drivers. This issue can be addressed using a reject inference technique that includes the characteristics of rejected applicants in the model. Due to the low numbers of accepted applicants and default records, credit scoring models usually face a class imbalance problem. However, previous literature on sample selection models for credit scoring does not address the class imbalance issue. To fill this gap, we extend the Generalised Extreme Value (GEV) regression model for binary data to the sample selection framework. We consider the quantile function of the GEV distribution as a link function in both the selection and outcome equations. We use the copula function to model the dependence structure between the two equations for its flexibility. This proposal is called the Sample Selection Generalised Extreme Value (SSGEV) model and it is implemented in the R package BivGEV. We apply this model to a comprehensive dataset provided by Lending Club, and we show that parameter estimates obtained only on accepted P2P applicants are biased and coherently with the literature. The SSGEV model achieves a higher predictive accuracy than those obtained using univariate approaches or a sample selection probit model. Our proposal also provides more conservative estimates of the Value-at-Risk and the Expected Shortfall.

Modeling pedestrians' activity time-use choices in a virtual urban public space: The influences of the environment and affective experience

Understanding pedestrians' time-use choices for multiple activities in urban public spaces is crucial for developing diverse and inclusive public spaces. Few studies have explored how pedestrians' time-use choices are influenced by the physical environment when engaging in various micro-level activities in public spaces, nor have they captured the influence of experience-based factors (e.g., emotion and perceptions) triggered by varying environments, as well as heterogeneity between individuals. This study employs the multiple discrete-continuous extreme value (MDCEV) model to estimate the effects of public space environmental attributes, visit purpose, emotion, and perceptions on individuals' activity time-use choices using data collected in varying virtual hypothetical public spaces. A latent class MDCEV model incorporating personal variables is used to further examine individual heterogeneity. The results indicate that outdoor dining spaces and benches significantly promote outdoor activities. Emotional pleasure and arousal, as well as perceived legibility and liveness, significantly influence various activities in varying ways and to varying degrees. Differences in activity time-use choice patterns between two groups are revealed - one more emotionally driven and the other more cognitively driven. The results complement existing knowledge of pedestrians' activities and inform the planning and design decisions for positive human-environment interactions in urban public spaces.

Fast and scalable inference for spatial extreme value models

Fast and scalable inference for spatial extreme value models

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

Extreme Value Theory (EVT) models have recently gained increasing popularity for crash risk estimation using traffic conflict data. Extreme value modeling consists of two fundamental approaches: the block maxima approach and the peak-over-threshold approach, each with several variants. However, a comprehensive comparison of these two approaches and their variants in crash risk estimation is lacking. This study bridges this gap by comparing different extreme value modeling techniques and evaluating their performance in estimating crash frequencies. Within a non-stationary Bayesian hierarchical modeling framework, the analyzed models include the block maxima model, the r largest order statistic model, and the peak-over-threshold model with the fixed and dynamic threshold, across univariate and bivariate traffic conflict cases. The analysis utilizes modified time-to-collision and post-encroachment time conflict indicator data collected from four signalized intersections in the City of Surrey, British Columbia, Canada. The results show that incorporating additional order statistics in the r largest order statistic model improves predictive performance, particularly with limited extreme conflict samples. Moreover, employing the dynamic threshold within the peak-over-threshold model enhances model goodness-of-fit and yields more accurate crash frequency estimates compared to using the fixed threshold. While the performance of the block maxima and peak-over-threshold models varies with the selected conflict indicator in the univariate case, the bivariate peak-over-threshold model with the dynamic threshold exhibits superior overall prediction accuracy over the corresponding block maxima model. This is likely due to the effectiveness of the dynamic threshold in precisely identifying truly critical extreme conflicts.