Gaining a better understanding of the factors that affect the likelihood of a vehicle crash has been an area of research focus for many decades. However, in the absence of detailed driving data that would help improve the identification of cause and effect relationships with individual vehicle crashes, most researchers have addressed this problem by framing it in terms of understanding the factors that affect the frequency of crashes - the number of crashes occurring in some geographical space (usually a roadway segment or intersection) over some specified time period. This paper provides a detailed review of the key issues associated with crash-frequency data as well as the strengths and weaknesses of the various methodological approaches that researchers have used to address these problems. While the steady march of methodological innovation (including recent applications of random parameter and finite mixture models) has substantially improved our understanding of the factors that affect crash-frequencies, it is the prospect of combining evolving methodologies with far more detailed vehicle crash data that holds the greatest promise for the future.

http://ceprofs.tamu.edu/dlord/Papers/Lord-Mannering_Review.pdf

The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives

This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].

Reliability Engineering and System Safety

Social Justice and the City

/pdf/the-black-swan-the-impact-of-the-highly-improbable-578rzpihbf.pdf

The Black Swan: The Impact of the Highly Improbable

https://www.ce.utexas.edu/prof/bhat/ABSTRACTS/AMAR_review_article.pdf

Analytic methods in accident research: Methodological frontier and future directions

Since the terrorist attacks on the United States on September 11th 2001, a large number of potential attack scenarios have been generated, and a number of responses have been implemented or suggested. The spectrum of possibilities, however, is extremely large, the amount of existing or potentially relevant information immense and confusing. The effectiveness of countermeasures can be difficult to assess in the absence of some quantification of the risks posed by different scenarios. We present in this paper a model for setting priorities among threats and among countermeasures, based on probabilistic risk analysis, decision analysis, and elements of game theory. This model accounts for the probabilities of different scenarios, the objectives of both the terrorists and the U.S., and the dynamic competition between them. In this paper, we use the rational decision analysis model in a descriptive mode on the terrorist side and in a prescriptive mode for the United States. Because we illustrate our model using fictitious numbers, the importance of this work is not so much in the specific ranking of countermeasures that it suggests as in the framework for reasoning that it provides. This includes analysis and fusion of data from many sources and with different levels of reliability to understand the situation, and explicit preferences to set priorities in the face of considerable uncertainty.

Probabilistic Modeling of Terrorist Threats: A Systems Analysis Approach to Setting Priorities Among Countermeasures

http://ceprofs.tamu.edu/dlord/Papers/Lord_et_al._COM-Poisson.pdf

Application of the Conway–Maxwell–Poisson generalized linear model for analyzing motor vehicle crashes

. In the past decade, machine learning methods for empirical rainfall–runoff modeling have seen extensive development and been proposed as a useful complement to physical hydrologic models, particularly in basins where data to support process-based models are limited. However, the majority of research has focused on a small number of methods, such as artificial neural networks, despite the development of multiple other approaches for non-parametric regression in recent years. Furthermore, this work has often evaluated model performance based on predictive accuracy alone, while not considering broader objectives, such as model interpretability and uncertainty, that are important if such methods are to be used for planning and management decisions. In this paper, we use multiple regression and machine learning approaches (including generalized additive models, multivariate adaptive regression splines, artificial neural networks, random forests, and M5 cubist models) to simulate monthly streamflow in five highly seasonal rivers in the highlands of Ethiopia and compare their performance in terms of predictive accuracy, error structure and bias, model interpretability, and uncertainty when faced with extreme climate conditions. While the relative predictive performance of models differed across basins, data-driven approaches were able to achieve reduced errors when compared to physical models developed for the region. Methods such as random forests and generalized additive models may have advantages in terms of visualization and interpretation of model structure, which can be useful in providing insights into physical watershed function. However, the uncertainty associated with model predictions under extreme climate conditions should be carefully evaluated, since certain models (especially generalized additive models and multivariate adaptive regression splines) become highly variable when faced with high temperatures.

/pdf/machine-learning-methods-for-empirical-streamflow-simulation-38eth615au.pdf

Machine learning methods for empirical streamflow simulation: a comparison of model accuracy, interpretability, and uncertainty in seasonal watersheds

This article compares statistical methods for modeling power outage durations during hurricanes and examines the predictive accuracy of these methods. Being able to make accurate predictions of power outage durations is valuable because the information can be used by utility companies to plan their restoration efforts more efficiently. This information can also help inform customers and public agencies of the expected outage times, enabling better collective response planning, and coordination of restoration efforts for other critical infrastructures that depend on electricity. In the long run, outage duration estimates for future storm scenarios may help utilities and public agencies better allocate risk management resources to balance the disruption from hurricanes with the cost of hardening power systems. We compare the out-of-sample predictive accuracy of five distinct statistical models for estimating power outage duration times caused by Hurricane Ivan in 2004. The methods compared include both regression models (accelerated failure time (AFT) and Cox proportional hazard models (Cox PH)) and data mining techniques (regression trees, Bayesian additive regression trees (BART), and multivariate additive regression splines). We then validate our models against two other hurricanes. Our results indicate that BART yields the best prediction accuracy and that it is possible to predict outage durations with reasonable accuracy.

Comparison and validation of statistical methods for predicting power outage durations in the event of hurricanes.

In many cases, risk and reliability analyses involve estimating the probabilities of discrete events such as hardware failures and occurrences of disease or death. There is often additional information in the form of explanatory variables that can be used to help estimate the likelihood of different numbers of events in the future through the use of an appropriate regression model, such as a generalized linear model. However, existing generalized linear models (GLM) are limited in their ability to handle the types of variance structures often encountered in using count data in risk and reliability analysis. In particular, standard models cannot handle both underdispersed data (variance less than the mean) and overdispersed data (variance greater than the mean) in a single coherent modeling framework. This article presents a new GLM based on a reformulation of the Conway-Maxwell Poisson (COM) distribution that is useful for both underdispersed and overdispersed count data and demonstrates this model by applying it to the assessment of electric power system reliability. The results show that the proposed COM GLM can provide as good of fits to data as the commonly used existing models for overdispered data sets while outperforming these commonly used models for underdispersed data sets.

Seth D. Guikema

Papers

Probabilistic Modeling of Terrorist Threats: A Systems Analysis Approach to Setting Priorities Among Countermeasures

Application of the Conway–Maxwell–Poisson generalized linear model for analyzing motor vehicle crashes

Machine learning methods for empirical streamflow simulation: a comparison of model accuracy, interpretability, and uncertainty in seasonal watersheds

Comparison and validation of statistical methods for predicting power outage durations in the event of hurricanes.

A flexible count data regression model for risk analysis.