87,167 research outputs found
A mixed-effect statistical model for before-after speed studies
No full textThis paper proposes an efficient methodology to conduct observational before-after studies for operating speed data. The employed method has some noteworthy strengths: (i) it can analyze data at a disaggregated level to properly account for variations in the speed profile; (ii) it considers the entire distribution of speed to overcome the bias associated to the traditional approaches that represent the speed distribution with a single point estimate; (iii) it takes advantage of full Bayes methods to avoid the empirical Bayes method limitations. To illustrate the feasibility of the proposed framework, a limited sample of before-after speed dataset from Montreal was used. The effectiveness of a safety countermeasure-a reduction in speed limits-was assessed. The speed data were collected on local urban streets grouped into comparison and treatment sites. For modeling the operating speed, we employed a hierarchical mixed-effect Binomial model using a wide range of site characteristics. This model is capable of dealing with heterogeneity across observations and accounting for site specific effects. The analyses results indicated that lane width, number of lanes, and night hours affect the operating speed positively while presence of parking, peak hours, weekend, one way, and precipitation affect it negatively. Although the speed limit reduction was found to be effective in controlling the operating speed, the analyzed sample may not be representative of the entire urban areas subject to this reduction. This paper also highlights some essential issues in the data collection process and the sensitivity of the outcomes to the collection method used.</p
On the largest eigenvalue of signed unicyclic graphs
No full textSigned graphs are graphs whose edges get signs ±1 and, as for unsigned graphs, they can be studied by means of graph matrices. Here we focus our attention to the largest eigenvalue, also known as the index of the adjacency matrix of signed graphs. Firstly we give some general results on the index variation when the corresponding signed graph is perturbed. Also, we determine signed graphs achieving the minimal or the maximal index in the class of unbalanced unicyclic graphs of order n≥3
Bayesian road safety analysis: Incorporation of past evidence and effect of hyper-prior choice
No full textProblem This paper aims to address two related issues when applying hierarchical Bayesian models for road safety analysis, namely: (a) how to incorporate available information from previous studies or past experiences in the (hyper) prior distributions for model parameters and (b) what are the potential benefits of incorporating past evidence on the results of a road safety analysis when working with scarce accident data (i.e., when calibrating models with crash datasets characterized by a very low average number of accidents and a small number of sites). Method A simulation framework was developed to evaluate the performance of alternative hyper-priors including informative and non-informative Gamma, Pareto, as well as Uniform distributions. Based on this simulation framework, different data scenarios (i.e., number of observations and years of data) were defined and tested using crash data collected at 3-legged rural intersections in California and crash data collected for rural 4-lane highway segments in Texas. Results This study shows how the accuracy of model parameter estimates (inverse dispersion parameter) is considerably improved when incorporating past evidence, in particular when working with the small number of observations and crash data with low mean. The results also illustrates that when the sample size (more than 100 sites) and the number of years of crash data is relatively large, neither the incorporation of past experience nor the choice of the hyper-prior distribution may affect the final results of a traffic safety analysis. Conclusions As a potential solution to the problem of low sample mean and small sample size, this paper suggests some practical guidance on how to incorporate past evidence into informative hyper-priors. By combining evidence from past studies and data available, the model parameter estimates can significantly be improved. The effect of prior choice seems to be less important on the hotspot identification. Impact on Industry The results show the benefits of incorporating prior information when working with limited crash data in road safety studies.</p
Using a flexible multivariate latent class approach to model correlated outcomes: A joint analysis of pedestrian and cyclist injuries
No full textSeveral recent transportation safety studies have indicated the importance of accounting for correlated outcomes, for example, among different crash types, including differing injury-severity levels. In this paper, we discuss inference for such data by introducing a flexible Bayesian multivariate model. In particular, we use a Dirichlet process mixture to keep the dependence structure unconstrained, relaxing the usual homogeneity assumptions. The resulting model collapses into a latent class multivariate model that is in the form of a flexible mixture of multivariate normal densities for which the number of mixtures (latent components) not only can be large but also can be inferred from the data as part of the analysis. Therefore, besides accounting for correlation among crash types through a heterogeneous correlation structure, the proposed model helps address unobserved heterogeneity through its latent class component. To our knowledge, this is the first study to propose and apply such a model in the transportation literature. We use the model to investigate the effects of various factors such as built environment characteristics on pedestrian and cyclist injury counts at signalized intersections in Montreal, modeling both outcomes simultaneously. We demonstrate that the homogeneity assumption of the standard multivariate model does not hold for the dataset used in this study. Consequently, we show how such a spurious assumption affects predictive performance of the model and the interpretation of the variables based on marginal effects. Our flexible model better captures the underlying complex structure of the correlated data, resulting in a more accurate model that contributes to a better understanding of safety correlates of non-motorist road users. This in turn helps decision-makers in selecting more appropriate countermeasures targeting vulnerable road users, promoting the mobility and safety of active modes of transportation.</p
Wavelets method for solving systems of nonlinear singular fractional Volterra integro-differential equations
No full textThis paper presents a computational method for solving a class of system of nonlinear singular
fractional Volterra integro-differential equations. First, existences of a unique solution
for under studying problem is proved. Then, shifted Chebyshev polynomials and
their properties are employed to derive a general procedure for forming the operational
matrix of fractional derivative for Chebyshev wavelets. The application of this operational
matrix for solving mentioned problem is explained. In the next step, the error analysis of
the proposed method is investigated. Finally, some examples are included for demonstrating
the efficiency of the proposed method
Bayesian nonparametric modeling in transportation safety studies: Applications in univariate and multivariate settings
No full textIn transportation safety studies, it is often necessary to account for unobserved heterogeneity and multimodality in data. The commonly used standard or over-dispersed generalized linear models (e.g., negative binomial models) do not fully address unobserved heterogeneity, assuming that crash frequencies follow unimodal exponential families of distributions. This paper employs Bayesian nonparametric Dirichlet process mixture models demonstrating some of their major advantages in transportation safety studies. We examine the performance of the proposed approach using both simulated and real data. We compare the proposed model with other models commonly used in road safety literature including the Poisson-Gamma, random effects, and conventional latent class models. We use pseudo Bayes factors as the goodness-of-fit measure, and also examine the performance of the proposed model in terms of replicating datasets with high proportions of zero crashes. In a multivariate setting, we extend the standard multivariate Poisson-lognormal model to a more flexible Dirichlet process mixture multivariate model. We allow for interdependence between outcomes through a nonparametric random effects density. Finally, we demonstrate how the robustness to parametric distributional assumptions (usually the multivariate normal density) can be examined using a mixture of points model when different (multivariate) outcomes are modeled jointly.</p
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