Some aspects of random utility, extreme value theory and multinomial logit models

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

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

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

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

The most commonly used variant of conjoint analysis is choice-based conjoint (CBC). Here, hierarchical Bayesian (HB) multinomial logit (MNL) models are widely used for preference estimation at the individual respondent level. A new and very flexible approach to address multimodal and skewed preference heterogeneity in the context of CBC is the Dirichlet Process Mixture (DPM) MNL model. The number and masses of components do not have to be predisposed like in the latent class (LC) MNL model or in the mixture-of-normals (MoN) MNL model. The aim of this Monte Carlo study is to evaluate the performance of Bayesian choice models (basic MNL, HB-MNL, MoN-MNL, LC-MNL and DPM-MNL models) under varying data conditions (especially under multimodal heterogeneity structures) using statistical criteria for parameter recovery, goodness-of-fit and predictive accuracy. The core finding from this Monte Carlo study is that the standard HB-MNL model appears to be highly robust in multimodal preference settings.

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

Energy prices are characterized by distributions that are asymmetric and that have heavier than Gaussian tails. Yet, many researchers continue to employ statistical methods that do not explicitly account for heavy tails and skewness in energy prices. In this chapter, we explicitly account for heavy tails and skewness with an application to electricity price risk using the Generalized Pareto Distribution and the Generalized Extreme Value Distribution. Specifically, we model value-at-risk (VaR) which is a widely-used measure of the maximum potential change in value of a portfolio of financial assets with a given probability over a given time horizon. VaR has become a standard measure of market risk and a common practice is to compute VaR by assuming that changes in value of the portfolio are conditionally normally distributed. However, assets returns usually come from heavy-tailed distributions, so computing VaR under the assumption of conditional normality can be an important source of error. We illustrate in our application to electric power, that VaR estimates based on extreme value theory models — in particular the generalized Pareto distribution — are more accurate than those produced by alternative models such as normality or historical simulation.

Mode choice behaviour is often modelled by discrete choice models, in which the utility of each mode is characterized by mode-specific parameters reflecting how strongly the utility of that mode depends on attributes such as travel speed and cost, and a mode-specific constant value. For new modes, the mode-specific parameters and the constant in the utility function of discrete choice models are not known and are difficult to estimate on the basis of stated preferences data/choice experiments and cannot be estimated on the basis of revealed preference data. This paper demonstrates how revealed preference data can be used to estimate a discrete mode choice model without using mode-specific constants and mode-specific parameters. This establishes a method that can be used to analyze any new mode using revealed preference data and discrete choice models and is demonstrated using the OViN 2017 dataset with trips throughout the Netherlands using a multinomial and nested logit model. This results in a utility function without any alternative specific constants or parameters, with a rho-squared of 0.828 and an accuracy of 0.758. The parameters from this model are used to calculate the future modal split of shared autonomous vehicles and electric steps, leading to a potential modal split range of 24–30% and 37–44% when using a multinomial logit model, and 15–20% and 33–40% when using a nested logit model. An overestimation of the future modal split occurs due to the partial similarities between different transport modes when using a multinomial logit model. It can therefore be concluded that a nested logit model is better suited for estimating the potential modal split of a future mode than a multinomial logit model. To the authors’ knowledge, this is the first time that the future modal split of shared autonomous vehicles and electric steps has been calculated using revealed preference data from existing modes using an unlabelled mode modelling approach.

This paper uses extreme value theory and exponential generalised autoregressive score models to estimate the tail extremes of financial return series. The peak‐over‐threshold method based on the generalised pareto distribution is combined with the EGAS models and the nonparametric quantile method is used to determine the thresholds in the POT method, which is used to calculate the value‐at‐risk of financial markets and to perform backtesting. The empirical analysis was conducted on the soybean oil, rapeseed oil, and palm oil futures indices in the Chinese futures market. The study demonstrated that the EGAS‐POT models based on nonparametric quantile thresholds can effectively characterise tail risk and provide a feasible measure of risk for investors.

We employed a cross-nested logit (CNL) model that permits a rich pattern of substitution among alternatives within a closed form choice model. The specification we employed is ideal for applications with many choice alternatives, such as the 431 fishing sites in this application. The CNL model provided a significant improvement over multinomial and nested logit model specifications at explaining observed recreational fishing site choices by residents of northern Ontario, Canada. Results from two scenarios illustrated the implications of using the CNL model on spatial substitution patterns and welfare measures associated with attribute change scenarios. The CNL model forecasts demonstrated that the relative change in fishing site use was lower at the most affected sites and higher at sites near the affected sites than was predicted by the multinomial logit model. No consistent pattern was found in mean or variance of welfare estimates associated with hypothetical attribute changes.

Travel mode imputation using GPS and accelerometer data from a multi-day travel survey

Sensitivity evaluation of machine learning-based calibrated transportation mode choice models: A case study of Alexandria City, Egypt

Statisticians along with other scientists have made significant computational advances that enable the estimation of formerly complex statistical models. The Bayesian inference framework combined with Markov chain Monte Carlo estimation methods such as the Gibbs sampler enable the estimation of discrete choice models such as the multinomial logit (MNL) model. MNL models are frequently applied in transportation research to model choice outcomes such as mode, destination, or route choices or to model categorical outcomes such as crash outcomes. Recent developments allow for the modification of the potentially limiting assumptions of MNL such as the independence from irrelevant alternatives (IIA) property. However, relatively little transportation-related research has focused on Bayesian MNL models, the tractability of which is of great value to researchers and practitioners alike. This paper addresses MNL model specification issues in the Bayesian framework, such as the value of including prior information on parameters, allowing for nonlinear covariate effects, and extensions to random parameter models, so changing the usual limiting IIA assumption. This paper also provides an example that demonstrates, using route-choice data, the considerable potential of the Bayesian MNL approach with many transportation applications. This paper then concludes with a discussion of the pros and cons of this Bayesian approach and identifies when its application is worthwhile.

Financial institutions have a large amount of data on their borrowers, which can be used to predict the probability of borrowers defaulting their loan or not. Some of the models that have been used to predict individual loan defaults include linear discriminant analysis models and extreme value theory models. These models are parametric in nature since they assume that the response being investigated takes a particular functional form. However, there is a possibility that the functional form used to estimate the response is very different from the actual functional form of the response. The purpose of this research was to analyze individual loan defaults in Kenya using the logistic regression model. The data used in this study was obtained from equity bank of Kenya for the period between 2006 to 2016. A random sample of 1000 loan applicants whose loans had been approved by equity bank of Kenya during this period was obtained. Data obtained was on the credit history, purpose of the loan, loan amount, nature of the saving account, employment status, sex of the applicant, age of the applicant, security used when acquiring the loan and the area of residence of the applicant (rural or urban). This study employed a quantitative research design, it deals with individual loans defaults as group characteristics of a borrower. The data was pre-processed by seeding using R- Software and then split into training dataset and test data set. The train data was used to train the logistic regression model by employing Supervised machine learning approach. The R-statistical software was used for the analysis of the data. The test data set was used to do cross-validation of the developed logistic model which later was used for analysis prediction of individual loan defaults. This study focused on the analysis of individual loan defaults in Kenya using the logistic regression model in Machine learning. The logistic regression model predicted 303 defaults from train data set, 122 non-defaults and misclassified loans were 56 and 69. The model had an accuracy of 0.7727 with the train data and 0.7333 with the test data. The logistic regression model showed a precision of 0.8440 and 0.8244 with the train and test data respectively. The performance of the model with both the train and test data was illustrated using a plot of train errors and test errors against sample size on the same axes. The plot showed that the performance of the model increases with an increase in sample size. The study recommended the use of logistic regression in conjunction with supervised machine learning approach in loan default prediction in financial institutions and also more research should be carried out on ensemble methods of loan defaults prediction in order to increase the prediction accuracy.

This study was conducted using daily precipitation records gathered at 37 meteorological stations in northern Xinjiang, China, from 1961 to 2010. We used the extreme value theory model, generalized extreme value (GEV) and generalized Pareto distribution (GPD), statistical distribution function to fit outputs of precipitation extremes with different return periods to estimate risks of precipitation extremes and diagnose aridity–humidity environmental variation and corresponding spatial patterns in northern Xinjiang. Spatiotemporal patterns of daily maximum precipitation showed that aridity–humidity conditions of northern Xinjiang could be well represented by the return periods of the precipitation data. Indices of daily maximum precipitation were effective in the prediction of floods in the study area. By analyzing future projections of daily maximum precipitation (2, 5, 10, 30, 50, and 100 years), we conclude that the flood risk will gradually increase in northern Xinjiang. GEV extreme value modeling yielded the best results, proving to be extremely valuable. Through example analysis for extreme precipitation models, the GEV statistical model was superior in terms of favorable analog extreme precipitation. The GPD model calculation results reflect annual precipitation. For most of the estimated sites’ 2 and 5-year T for precipitation levels, GPD results were slightly greater than GEV results. The study found that extreme precipitation reaching a certain limit value level will cause a flood disaster. Therefore, predicting future extreme precipitation may aid warnings of flood disaster. A suitable policy concerning effective water resource management is thus urgently required.