O problema de testar hipóteses sobre proporções marginais de uma tabela de contingência assume papel fundamental, por exemplo, na investigação da mudança de opinião e comportamento. Apesar disso, a maioria dos textos na literatura abordam procedimentos para populações independentes, como o teste de homogeneidade de proporções. Existem alguns trabalhos que exploram testes de hipóteses em caso de respostas dependentes como, por exemplo, o teste de McNemar para tabelas 2 x 2. A extensão desse teste para tabelas k x k, denominado teste de homogeneidade marginal, usualmente requer, sob a abordagem clássica, a utilização de aproximações assintóticas. Contudo, quando o tamanho amostral é pequeno ou os dados esparsos, tais métodos podem eventualmente produzir resultados imprecisos. Neste trabalho, revisamos medidas de evidência clássicas e bayesianas comumente empregadas para comparar duas proporções marginais. Além disso, desenvolvemos o Full Bayesian Significance Test (FBST) para testar a homogeneidade marginal em tabelas de contingência bidimensionais e multidimensionais. O FBST é baseado em uma medida de evidência, denominada e-valor, que não depende de resultados assintóticos, não viola o princípio da verossimilhança e respeita a várias propriedades lógicas esperadas para testes de hipóteses. Consequentemente, a abordagem ao problema de teste de homogeneidade marginal pelo FBST soluciona diversas limitações geralmente enfrentadas por outros procedimentos. / Tests of hypotheses for marginal proportions in contingency tables play a fundamental role, for instance, in the investigation of behaviour (or opinion) change. However, most texts in the literature are concerned with tests that assume independent populations (e.g: homogeneity tests). There are some works that explore hypotheses tests for dependent proportions such as the McNemar Test for 2 x 2 contingency tables. The generalization of McNemar test for k x k contingency tables, called marginal homogeneity test, usually requires asymptotic approximations. Nevertheless, for small sample sizes or sparse tables, such methods may occasionally produce imprecise results. In this work, we review some classical and Bayesian measures of evidence commonly applied to compare two marginal proportions. We propose the Full Bayesian Significance Test (FBST) to investigate marginal homogeneity in two-way and multidimensional contingency tables. The FBST is based on a measure of evidence, called e-value, which does not depend on asymptotic results, does not violate the likelihood principle and satisfies logical properties that are expected from hypothesis testing. Consequently, the FBST approach to test marginal homogeneity overcomes several limitations usually met by other procedures.

O problema de testar hipóteses sobre proporções marginais de uma tabela de contingência assume papel fundamental, por exemplo, na investigação da mudança de opinião e comportamento. Apesar disso, a maioria dos textos na literatura abordam procedimentos para populações independentes, como o teste de homogeneidade de proporções. Existem alguns trabalhos que exploram testes de hipóteses em caso de respostas dependentes como, por exemplo, o teste de McNemar para tabelas 2 x 2. A extensão desse teste para tabelas k x k, denominado teste de homogeneidade marginal, usualmente requer, sob a abordagem clássica, a utilização de aproximações assintóticas. Contudo, quando o tamanho amostral é pequeno ou os dados esparsos, tais métodos podem eventualmente produzir resultados imprecisos. Neste trabalho, revisamos medidas de evidência clássicas e bayesianas comumente empregadas para comparar duas proporções marginais. Além disso, desenvolvemos o Full Bayesian Significance Test (FBST) para testar a homogeneidade marginal em tabelas de contingência bidimensionais e multidimensionais. O FBST é baseado em uma medida de evidência, denominada e-valor, que não depende de resultados assintóticos, não viola o princípio da verossimilhança e respeita a várias propriedades lógicas esperadas para testes de hipóteses. Consequentemente, a abordagem ao problema de teste de homogeneidade marginal pelo FBST soluciona diversas limitações geralmente enfrentadas por outros procedimentos. / Tests of hypotheses for marginal proportions in contingency tables play a fundamental role, for instance, in the investigation of behaviour (or opinion) change. However, most texts in the literature are concerned with tests that assume independent populations (e.g: homogeneity tests). There are some works that explore hypotheses tests for dependent proportions such as the McNemar Test for 2 x 2 contingency tables. The generalization of McNemar test for k x k contingency tables, called marginal homogeneity test, usually requires asymptotic approximations. Nevertheless, for small sample sizes or sparse tables, such methods may occasionally produce imprecise results. In this work, we review some classical and Bayesian measures of evidence commonly applied to compare two marginal proportions. We propose the Full Bayesian Significance Test (FBST) to investigate marginal homogeneity in two-way and multidimensional contingency tables. The FBST is based on a measure of evidence, called e-value, which does not depend on asymptotic results, does not violate the likelihood principle and satisfies logical properties that are expected from hypothesis testing. Consequently, the FBST approach to test marginal homogeneity overcomes several limitations usually met by other procedures.

The research conducted in this thesis consists of a Geographic Information Systems (GIS) based safety study and a spatial analysis of vehicle crashes in the State of Florida. The GIS safety study is comprised of a County and Roadway Level GIS analysis of multilane corridors. The spatial analysis investigated the use of county-level vehicle crash models, taking spatial effects into account. The GIS safety study examines the locations of high trends of severe crashes (includes incapacitating and fatal crashes) on multilane corridors in the State of Florida at two levels, county level and roadway level. The GIS tool, which is used frequently in traffic safety research, was utilized to visually display those locations. At the county level, several maps of crash trends were generated. It was found that counties with high population and large metropolitan areas tend to have more crash occurrences. It was also found that the most severe crashes occurred in counties with more urban than rural roads. The neighboring counties of Pasco, Pinellas and Hillsborough had high severe crash rate per mile. At the roadway level, seven counties were chosen for the analysis based on their high severe crash trends, metropolitan size and geographical location. Several GIS maps displaying the safety level of multilane corridors in the seven counties were generated. The GIS maps were based on a ranking methodology that was developed in research that evaluated the safety condition of road segments and signalized intersections separately. The GIS maps were supported by Excel tables which provided details on the most hazardous locations on the roadways. The results of the roadway level analysis found that the worst corridors were located in Pasco, Pinellas and Hillsborough Counties. Also, a sliding window approach was developed and performed on the ten most hazardous corridors of the seven counties. The results were graphs locating the most dangerous 0.5 miles on a corridor. For the spatial analysis of crashes, the exploratory Moran's I statistic test revealed that crash related spatial clustering existed at the county level. For crash modeling, a full Bayesian (FB) hierarchical model is proposed to account for the possible spatial correlation among crash occurrence of adjacent counties. The spatial correlation is realized by specifying a Conditional Auto-regressive prior to the residual term of the link function in standard Poisson regression. Two FB models were developed, one for total crashes and one for severe crashes. The variables used include traffic related factors and socio-economic factors. Counties with higher road congestion levels, higher densities of arterials and intersections, higher percentage of population in the 15-24 age group and higher income levels have increased crash risk. Road congestion and higher education levels, however, were negatively correlated with the risk of severe crashes. The analysis revealed that crash related spatial correlation existed among the counties. The FB models were found to fit the data better than traditional methods such as Negative Binomial and that is primarily due to the existence of spatial correlation. Overall, this study provides the Transportation Agencies with specific information on where improvements must be implemented to have better safety conditions on the roads of Florida. The study also proves that neighboring counties are more likely to have similar crash trends than the more distant ones.

This thesis comprises two studies that investigated bike infrastructure safety in North America. The first study conducted a corridor-level analysis to quantify the safety of different bike infrastructure types and assess the influence of corridor-specific characteristics on their performance. Using a Poisson-lognormal Full Bayesian model, the study analyzed fatal and injury bike-vehicle collisions on over 7800 corridors in Toronto, Canada. The findings revealed that bike infrastructure effectively reduces bike collisions, with cycle tracks demonstrating superior safety benefits due to the physical separation of cyclists from vehicular traffic. Cycle tracks were found to be particularly effective on long corridors with fewer intersections as bike-vehicle interactions along the corridor are minimized. Signed routes were safe on low-volume and low-speed roads, while bike lanes are more suited for a short section of high-volume corridors with a high intersection density. The second study assessed the safety of parking-protected bike lanes (PPBL), a new concept that is rapidly growing in North America. Utilizing data from nineteen street sections in Vancouver and Ottawa, the study developed a Full Bayesian Before-and-after model to evaluate the safety impacts of converting traditional painted bike lanes to PPBLs. The results indicated a significant reduction of 31.2% in total collisions after PPBL implementation. However, the effects of PPBLs on cyclist safety were found to be sensitive to factors such as bike path opening density, intersection density, and intersection treatments. In roads where proper intersection treatments and minimal protection of PPBL openings can be provided, painted bike lanes can be converted into PPBLs, and significant safety benefits can be expected. The findings of this thesis offer practical guidance for city planners and policymakers regarding the safety implications of different bike infrastructure types and the most appropriate conditions to implement them, which supports bike safety enhancement initiatives and attracts more people to bike. / Thesis / Master of Applied Science (MASc) / This thesis presents two studies that offer valuable insights to improve bike safety. The first study examined the safety of various bike infrastructure types along with the impact of corridor characteristics on their performance. The findings emphasized the effectiveness of cycle tracks in reducing collisions on long corridors with fewer intersections. Signed routes were found to be effective on low-volume and low-speed roads, while bike lanes were ideal on short sections of high-volume roads with a high intersection density. The second study assessed the impacts of new designed concept, known as the parking-protected bike lanes (PPBLs). The study showed that converting painted bike lanes to PPBLs significantly reduced total collisions. However, proper treatment of intersection and bikeway openings is crucial for enhancing cyclist safety and reducing multi-vehicle rear-end collisions. Where proper intersection treatment and minimal protection of bikeway openings can be provided, bike lanes can be safely converted into PPBLs.

Both traffic congestion and road accidents impose a burden on society, and it is therefore important for transport policy makers to reduce their impact. An ideal scenario would be that traffic congestion and accidents are reduced simultaneously, however, this may not be possible since it has been speculated that increased traffic congestion may be beneficial in terms of road safety. This is based on the premise that there would be fewer fatal accidents and the accidents that occurred would tend to be less severe due to the low average speed when congestion is present. If this is confirmed then it poses a potential dilemma for transport policy makers: the benefit of reducing congestion might be off-set by more severe accidents. It is therefore important to fully understand the relationship between traffic congestion and road accidents while controlling for other factors affecting road traffic accidents. The relationship between traffic congestion and road accidents appears to be an under researched area. Previous studies often lack a suitable congestion measurement and an appropriate econometric model using real-world data. This thesis aims to explore the relationship between traffic congestion and road accidents by using an econometric and GIS approach. The analysis is based on the data from the M25 motorway and its surrounding major roads for the period 2003-2007. A series of econometric models have been employed to investigate the effect of traffic congestion on both accident frequency (such as classical Negative Binomial and Bayesian spatial models) and accident severity (such as ordered logit and mixed logit models). The Bayesian spatial model and the mixed logit model are the best models estimated for accident frequency and accident severity analyses respectively. The model estimation results suggest that traffic congestion is positively associated with the frequency of fatal and serious injury accidents and negatively (i.e. inversely) associated with the severity of accidents that have occurred. Traffic congestion is found to have little impact on the frequency of slight injury accidents. Other contributing factors have also been controlled for and produced results consistent with previous studies. It is concluded that traffic congestion overall has a negative impact on road safety. This may be partially due to higher speed variance among vehicles within and between lanes and erratic driving behaviour in the presence of congestion. The results indicate that mobility and safety can be improved simultaneously, and therefore there is significant additional benefit of reducing traffic congestion in terms of road safety. Several policy implications have been identified in order to optimise the traffic flow and improve driving behaviour, which would be beneficial to both congestion and accident reduction. This includes: reinforcing electronic warning signs and the Active Traffic Management, enforcing average speed on a stretch of a roadway and introducing minimum speed limits in the UK. This thesis contributes to knowledge in terms of the relationship between traffic congestion and road accidents, showing that mobility and safety can be improved simultaneously. A new hypothesis is proposed that traffic congestion on major roads may increase the occurrence of serious injury accidents. This thesis also proposes a new map-matching technique so as to assign accidents to the correct road segments, and shows how a two-stage modelling process which combines both accident frequency and severity models can be used in site ranking with the objective of identifying hazardous accident hotspots for further safety examination and treatment.

Pfeffermann, Krieger e Rinott (1998) apresentaram uma metodologia para modelar processos de amostragem que pode ser utilizada para avaliar se este processo de amostragem é informativo. Neste cenário, as probabilidades de seleção da amostra são aproximadas por uma função polinomial dependendo das variáveis resposta e concomitantes. Nesta abordagem, nossa principal proposta é investigar a aplicação do teste de significância FBST (Full Bayesian Significance Test), apresentado por Pereira e Stern (1999), como uma ferramenta para testar a ignorabilidade amostral, isto é, para avaliar uma relação de significância entre as probabilidades de seleção da amostra e a variável resposta. A performance desta modelagem estatística é testada com alguns experimentos computacionais. / Pfeffermann, Krieger and Rinott (1998) introduced a framework for modeling sampling processes that can be used to assess if a sampling process is informative. In this setting, sample selection probabilities are approximated by a polynomial function depending on outcome and auxiliary variables. Within this framework, our main purpose is to investigate the application of the Full Bayesian Significance Test (FBST), introduced by Pereira and Stern (1999), as a tool for testing sampling ignorability, that is, to detect a significant relation between the sample selection probabilities and the outcome variable. The performance of this statistical modelling framework is tested with some simulation experiments.

Pfeffermann, Krieger e Rinott (1998) apresentaram uma metodologia para modelar processos de amostragem que pode ser utilizada para avaliar se este processo de amostragem é informativo. Neste cenário, as probabilidades de seleção da amostra são aproximadas por uma função polinomial dependendo das variáveis resposta e concomitantes. Nesta abordagem, nossa principal proposta é investigar a aplicação do teste de significância FBST (Full Bayesian Significance Test), apresentado por Pereira e Stern (1999), como uma ferramenta para testar a ignorabilidade amostral, isto é, para avaliar uma relação de significância entre as probabilidades de seleção da amostra e a variável resposta. A performance desta modelagem estatística é testada com alguns experimentos computacionais. / Pfeffermann, Krieger and Rinott (1998) introduced a framework for modeling sampling processes that can be used to assess if a sampling process is informative. In this setting, sample selection probabilities are approximated by a polynomial function depending on outcome and auxiliary variables. Within this framework, our main purpose is to investigate the application of the Full Bayesian Significance Test (FBST), introduced by Pereira and Stern (1999), as a tool for testing sampling ignorability, that is, to detect a significant relation between the sample selection probabilities and the outcome variable. The performance of this statistical modelling framework is tested with some simulation experiments.

Made available in DSpace on 2016-06-02T20:06:02Z (GMT). No. of bitstreams: 1 2203.pdf: 1300161 bytes, checksum: 2c1f11d939eab9ab849bb04bf2363a53 (MD5) Previous issue date: 2009-02-10 / Financiadora de Estudos e Projetos / This study considers two discrete distributions based on Bernoulli trials: the Binomial and the Negative Binomial. We explore credibility and confidence intervals to estimate the probability of success of each distribution. The main goal is to analyze their performance coverage probability and average range across the parametric space. We also consider point analysis of bayesian estimators and maximum likelihood estimators, whose interest is to confirm through simulation their consistency, bias and mean square error. In this paper the Objective Bayesian Inference is applied through the noninformative Bayes-Laplace prior, Haldane prior, reference prior and least favorable prior. By analyzing the prior distributions in the minimax decision theory context we verified that the least favorable prior distribution has every other considered prior distributions as particular cases when a quadratic loss function is applied, and matches the Bayes-Laplace prior in considering the quadratic weighed loss function for the Binomial model (which was never found in literature). We used the noninformative Bayes-Laplace prior and Jeffreys prior for the Negative Binomial model. Our findings show through coverage probability, average range of bayesian intervals and point estimation that the Objective Bayesian Inference has good frequentist properties for the probability of success of Binomial and Negative Binomial models. The last stage of this study discusses the presence of correlated proportions in matched-pairs (2 × 2 table) of Bernoulli with the goal of obtaining more information in relation of the considered measures for testing the occurrence of correlated proportions. In this sense the Trinomial model and the partial likelihood function were used from the frequentist and bayesian point of view. The Full Bayesian Significance Test (FBST) was used for real data sets and was shown sensitive to parameterization, however, this study was not possible for the frequentist method since distinct methods are needed to be applied to Trinomial model and the partial likelihood function. / Neste estudo são abordadas duas distribuições discretas baseadas em ensaios de Bernoulli, a Binomial e a Binomial Negativa. São explorados intervalos de credibilidade e confiança para estimação da probabilidade de sucesso de ambas as distribuições. A principal finalidade é analisar nos contextos clássico e bayesiano o desempenho da probabilidade de cobertura e amplitude média gerada pelos intervalos de confiança e intervalos de credibilidade ao longo do espaço paramétrico. Considerou-se também a análise dos estimadores pontuais bayesianos e o estimador de máxima verossimilhança, cujo interesse é confirmar por meio de simulação a consistência e calcular o viés e o erro quadrático médio dos mesmos. A Inferência Bayesiana Objetiva é empregada neste estudo por meio das distribuições a priori não-informativas de Bayes-Laplace, de Haldane, de Jeffreys e menos favorável. Ao analisar as distribuições a priori no contexto de teoria de decisões minimax, a distribuição a priori menos favorável resgata as demais citadas ao empregar a função de perda quadrática e coincide com a distribuição a priori de Bayes-Laplace ao considerar a função de perda quadrática ponderada para o modelo Binomial, o que não foi encontrado até o momento na literatura. Para o modelo Binomial Negativa são consideradas as distribuições a priori não-informativas de Bayes-Laplace e de Jeffreys. Com os estudos desenvolvidos pôde-se observar que a Inferência Bayesiana Objetiva para a probabilidade de sucesso dos modelos Binomial e Binomial Negativa apresentou boas propriedades freqüentistas, analisadas a partir da probabilidade de cobertura e amplitude média dos intervalos bayesianos e por meio das propriedades dos estimadores pontuais. A última etapa do trabalho consiste na análise da ocorrência de proporções correlacionadas em pares de eventos de Bernoulli (tabela 2×2) com a finalidade de determinar um possível ganho de informação em relação as medidas consideradas para testar a ocorrência de proporções correlacionadas. Para tanto fez-se uso do modelo Trinomial e da função de verossimilhança parcial tanto numa abordagem clássica quanto bayesiana. Nos conjuntos de dados analisados observou-se a medida de evidência bayesiana (FBST) como sensível à parametrização, já para os métodos clássicos essa comparação não foi possível, pois métodos distintos precisam ser aplicados para o modelo Trinomial e para a função de verossimilhança parcial.

High speed facilities are considered the backbone of any successful transportation system; Interstates, freeways, and expressways carry the majority of daily trips on the transportation network. Although these types of roads are relatively considered the safest among other types of roads, they still experience many crashes, many of which are severe, which not only affect human lives but also can have tremendous economical and social impacts. These facts signify the necessity of enhancing the safety of these high speed facilities to ensure better and efficient operation. Safety problems could be assessed through several approaches that can help in mitigating the crash risk on long and short term basis. Therefore, the main focus of the research in this dissertation is to provide a framework of risk assessment to promote safety and enhance mobility on freeways and expressways. Multi-level Safety Performance Functions (SPFs) were developed at the aggregate level using historical crash data and the corresponding exposure and risk factors to identify and rank sites with promise (hot-spots). Additionally, SPFs were developed at the disaggregate level utilizing real-time weather data collected from meteorological stations located at the freeway section as well as traffic flow parameters collected from different detection systems such as Automatic Vehicle Identification (AVI) and Remote Traffic Microwave Sensors (RTMS). These disaggregate SPFs can identify real-time risks due to turbulent traffic conditions and their interactions with other risk factors. In this study, two main datasets were obtained from two different regions. Those datasets comprise historical crash data, roadway geometrical characteristics, aggregate weather and traffic parameters as well as real-time weather and traffic data. iii At the aggregate level, Bayesian hierarchical models with spatial and random effects were compared to Poisson models to examine the safety effects of roadway geometrics on crash occurrence along freeway sections that feature mountainous terrain and adverse weather. At the disaggregate level; a main framework of a proactive safety management system using traffic data collected from AVI and RTMS, real-time weather and geometrical characteristics was provided. Different statistical techniques were implemented. These techniques ranged from classical frequentist classification approaches to explain the relationship between an event (crash) occurring at a given time and a set of risk factors in real time to other more advanced models. Bayesian statistics with updating approach to update beliefs about the behavior of the parameter with prior knowledge in order to achieve more reliable estimation was implemented. Also a relatively recent and promising Machine Learning technique (Stochastic Gradient Boosting) was utilized to calibrate several models utilizing different datasets collected from mixed detection systems as well as real-time meteorological stations. The results from this study suggest that both levels of analyses are important, the aggregate level helps in providing good understanding of different safety problems, and developing policies and countermeasures to reduce the number of crashes in total. At the disaggregate level, real-time safety functions help toward more proactive traffic management system that will not only enhance the performance of the high speed facilities and the whole traffic network but also provide safer mobility for people and goods. In general, the proposed multi-level analyses are useful in providing roadway authorities with detailed information on where countermeasures must be implemented and when resources should be devoted. The study also proves that traffic data collected from different detection systems could be a useful asset that should be utilized iv appropriately not only to alleviate traffic congestion but also to mitigate increased safety risks. The overall proposed framework can maximize the benefit of the existing archived data for freeway authorities as well as for road users.