Motor vehicle crashes are one of the leading causes of death in the United States. Traffic safety research targets at understanding the cause of crash, preventing the crash, and mitigating crash severity. This dissertation focuses on the driver-related traffic safety issues, in particular, on developing and implementing contemporary statistical modeling techniques on driving risk research on Naturalistic Driving Study data. The dissertation includes 5 chapters. In Chapter 1, I introduced the backgrounds of traffic safety research and naturalistic driving study. In Chapter 2, the state-of-practice statistical methods were implemented on individual driver risk assessment using NDS data. The study showed that critical-incident events and driver demographic characteristics can serve as good predictors for identifying risky drivers. In Chapter 3, I developed and evaluated a novel Bayesian random exposure method for Poisson regression models to account for situations where the exposure information needs to be estimated. Simulation studies and real data analysis on Cellphone Pilot Analysis study data showed that, random exposure models have significantly better model fitting performances and higher parameter coverage probabilities as compared to traditional fixed exposure models. The advantage is more apparent when the values of Poisson regression coefficients are large. In Chapter 4, I performed comprehensive simulation-based performance analyses to investigate the type-I error, power and coverage probabilities on summary effect size in classical meta-analysis models. The results shed some light for reference on the prospective and retrospective performance analysis in meta-analysis research. In Chapter 5, I implemented classical- and Bayesian-approach multi-group hierarchical models on 100-Car data. Simulation-based retrospective performance analyses were used to investigate the powers and parameter coverage probabilities among different hierarchical models. The results showed that under fixed-effects model context, complex secondary tasks are associated with higher driving risk. / Ph. D.

In this thesis, a dynamic spatial model for the spread of Chronic Wasting Disease in Colorado mule deer is derived from a system of differential equations that captures the qualitative spatial and temporal behaviour of the disease. These differential equations are incorporated into an empirical Bayesian hierarchical model through the unusual step of deterministic autoregressive updates. Spatial effects in the model are described directly in the differential equations rather than through the use of correlations in the data. The use of deterministic updates is a simplification that reduces the number of parameters that must be estimated, yet still provides a flexible model that gives reasonable predictions for the disease. The posterior distribution generated by the data model hierarchy possesses characteristics that are atypical for many Markov chain Monte Carlo simulation techniques. To address these difficulties, a new MCMC technique is developed that has qualities similar to recently introduced tempered Langevin type algorithms. The methodology is used to fit the CWD model, and posterior parameter estimates are then used to obtain predictions about Chronic Wasting Disease.

京都大学 / 新制・課程博士 / 博士(医科学) / 甲第25204号 / 医科博第160号 / 京都大学大学院医学研究科医科学専攻 / (主査)教授 佐藤 俊哉, 教授 古川 壽亮, 教授 武藤 学 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

Doctor of Philosophy / With the fast development of artificial intelligence (AI) technology, the reliability of AI needs to be investigated for confidently using AI products in our daily lives. This dissertation includes three projects introducing the statistical models and model estimation methods that can be used in the reliability analysis of AI systems. The first project analyzes the recurrent events data from autonomous vehicles (AVs). A nonparametric model is proposed to study the reliability of AI systems in AVs, and a statistical framework is introduced to evaluate the adequacy of using traditional parametric models in the analysis. The proposed model and framework are then applied to analyze AV data from four manufacturers that participated in an AV driving testing program overseen by the California Department of Motor Vehicles. The second project develops a survival model to investigate the failure times of graphics processing units (GPUs) used in supercomputers. The model considers several covariates, the spatial correlation, and the correlation among multiple types of failures. In addition, unique spatial correlation functions and a special distance function are introduced to quantify the spatial correlation inside supercomputers. The model is applied to explore the GPU failure times in the Titan supercomputer. The third project proposes a new Markov chain Monte Carlo sampler that can be used in the estimation and inference of spatial survival models. The sampler can generate a reasonable amount of samples within a shorter computing time compared with existing popular samplers. Important factors that can influence the performance of the proposed sampler are explored, and the sampler is used to analyze the Titan GPU failures to illustrate its usefulness in solving real-world problems.

La théorie statistique univariée des valeurs extrêmes se généralise au cas multivarié mais l'absence d'un cadre paramétrique naturel complique l'inférence de la loi jointe des extrêmes. Les marges d'erreur associée aux estimateurs non paramétriques de la structure de dépendance sont difficilement accessibles à partir de la dimension trois. Cependant, quantifier l'incertitude est d'autant plus important pour les applications que le problème de la rareté des données extrêmes est récurrent, en particulier en hydrologie. L'objet de cette thèse est de développer des modèles de dépendance entre extrêmes, dans un cadre bayésien permettant de représenter l'incertitude. Le chapitre 2 explore les propriétés des modèles obtenus en combinant des modèles paramétriques existants, par mélange bayésien (Bayesian Model Averaging BMA). Un modèle semi-paramétrique de mélange de Dirichlet est étudié au chapitre suivant : une nouvelle paramétrisation est introduite afin de s'affranchir d'une contrainte de moments caractéristique de la structure de dépendance et de faciliter l'échantillonnage de la loi à posteriori. Le chapitre 4 est motivé par une application hydrologique : il s'agit d'estimer la structure de dépendance spatiale des crues extrêmes dans la région cévenole des Gardons en utilisant des données historiques enregistrées en quatre points. Les données anciennes augmentent la taille de l'échantillon mais beaucoup de ces données sont censurées. Une méthode d'augmentation de données est introduite, dans le cadre du mélange de Dirichlet, palliant l'absence d'expression explicite de la vraisemblance censurée. Les conclusions et perspectives sont discutées au chapitre 5 / Uni-variate extreme value theory extends to the multivariate case but the absence of a natural parametric framework for the joint distribution of extremes complexifies inferential matters. Available non parametric estimators of the dependence structure do not come with tractable uncertainty intervals for problems of dimension greater than three. However, uncertainty estimation is all the more important for applied purposes that data scarcity is a recurrent issue, particularly in the field of hydrology. The purpose of this thesis is to develop modeling tools for the dependence structure between extremes, in a Bayesian framework that allows uncertainty assessment. Chapter 2 explores the properties of the model obtained by combining existing ones, in a Bayesian Model Averaging framework. A semi-parametric Dirichlet mixture model is studied next : a new parametrization is introduced, in order to relax a moments constraint which characterizes the dependence structure. The re-parametrization significantly improves convergence and mixing properties of the reversible-jump algorithm used to sample the posterior. The last chapter is motivated by an hydrological application, which consists in estimating the dependence structure of floods recorded at four neighboring stations, in the ‘Gardons’ region, southern France, using historical data. The latter increase the sample size but most of them are censored. The lack of explicit expression for the likelihood in the Dirichlet mixture model is handled by using a data augmentation framework

This paper uses Bayesian model comparison methods to simultaneously specify both the spatial weight structure and explanatory variables for a spatial growth regression involving 255 NUTS 2 regions across 25 European countries. In addition, a correct interpretation of the spatial regression parameter estimates that takes into account the simultaneous feed- back nature of the spatial autoregressive model is provided. Our findings indicate that incorporating model uncertainty in conjunction with appropriate parameter interpretation decreased the importance of explanatory variables traditionally thought to exert an important influence on regional income growth rates. (authors' abstract)

This paper uses Bayesian Model Averaging (BMA) to find robust determinants of economic growth in a new dataset of 255 European regions between 1995 and 2005. The paper finds that income convergence between countries is dominated by the catching-up of regions in new member states in Central and Eastern Europe (CEE), whereas convergence within countries is driven by regions in old EU member states. Regions containing capital cities are growing faster, particularly in CEE countries, as do regions with a large share of workers with higher education. The results are robust to allowing for spatial spillovers among European regions.

Understanding the determinants of aggregated default probabilities (PDs) has attracted substantial research over the past decades. This study addresses two major difficulties in understanding the determinants of aggregate PDs: Model uncertainty and multicollinearity among the regressors. We present Bayesian Model Averaging (BMA) as a powerful tool that overcomes model uncertainty. Furthermore, we supplement BMA with ridge regression to mitigate multicollinearity. We apply our approach to an Austrian dataset. Our findings suggest that factor prices like short term interest rates and energy prices constitute major drivers of default rates, while firms' profits reduce the expected number of failures. Finally, we show that the results of our baseline model are fairly robust to the choice of the prior model size. / Series: Research Report Series / Department of Statistics and Mathematics

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Cette thèse présente des méthodes de traitement de données de comptage en particulier et des données discrètes en général. Il s'inscrit dans le cadre d'un projet stratégique du CRNSG, nommé CC-Bio, dont l'objectif est d'évaluer l'impact des changements climatiques sur la répartition des espèces animales et végétales. Après une brève introduction aux notions de biogéographie et aux modèles linéaires mixtes généralisés aux chapitres 1 et 2 respectivement, ma thèse s'articulera autour de trois idées majeures. Premièrement, nous introduisons au chapitre 3 une nouvelle forme de distribution dont les composantes ont pour distributions marginales des lois de Poisson ou des lois de Skellam. Cette nouvelle spécification permet d'incorporer de l'information pertinente sur la nature des corrélations entre toutes les composantes. De plus, nous présentons certaines propriétés de ladite distribution. Contrairement à la distribution multidimensionnelle de Poisson qu'elle généralise, celle-ci permet de traiter les variables avec des corrélations positives et/ou négatives. Une simulation permet d'illustrer les méthodes d'estimation dans le cas bidimensionnel. Les résultats obtenus par les méthodes bayésiennes par les chaînes de Markov par Monte Carlo (CMMC) indiquent un biais relatif assez faible de moins de 5% pour les coefficients de régression des moyennes contrairement à ceux du terme de covariance qui semblent un peu plus volatils. Deuxièmement, le chapitre 4 présente une extension de la régression multidimensionnelle de Poisson avec des effets aléatoires ayant une densité gamma. En effet, conscients du fait que les données d'abondance des espèces présentent une forte dispersion, ce qui rendrait fallacieux les estimateurs et écarts types obtenus, nous privilégions une approche basée sur l'intégration par Monte Carlo grâce à l'échantillonnage préférentiel. L'approche demeure la même qu'au chapitre précédent, c'est-à-dire que l'idée est de simuler des variables latentes indépendantes et de se retrouver dans le cadre d'un modèle linéaire mixte généralisé (GLMM) conventionnel avec des effets aléatoires de densité gamma. Même si l'hypothèse d'une connaissance a priori des paramètres de dispersion semble trop forte, une analyse de sensibilité basée sur la qualité de l'ajustement permet de démontrer la robustesse de notre méthode. Troisièmement, dans le dernier chapitre, nous nous intéressons à la définition et à la construction d'une mesure de concordance donc de corrélation pour les données augmentées en zéro par la modélisation de copules gaussiennes. Contrairement au tau de Kendall dont les valeurs se situent dans un intervalle dont les bornes varient selon la fréquence d'observations d'égalité entre les paires, cette mesure a pour avantage de prendre ses valeurs sur (-1;1). Initialement introduite pour modéliser les corrélations entre des variables continues, son extension au cas discret implique certaines restrictions. En effet, la nouvelle mesure pourrait être interprétée comme la corrélation entre les variables aléatoires continues dont la discrétisation constitue nos observations discrètes non négatives. Deux méthodes d'estimation des modèles augmentés en zéro seront présentées dans les contextes fréquentiste et bayésien basées respectivement sur le maximum de vraisemblance et l'intégration de Gauss-Hermite. Enfin, une étude de simulation permet de montrer la robustesse et les limites de notre approche. / This thesis presents some estimation methods and algorithms to analyse count data in particular and discrete data in general. It is also part of an NSERC strategic project, named CC-Bio, which aims to assess the impact of climate change on the distribution of plant and animal species in Québec. After a brief introduction to the concepts and definitions of biogeography and those relative to the generalized linear mixed models in chapters 1 and 2 respectively, my thesis will focus on three major and new ideas. First, we introduce in chapter 3 a new form of distribution whose components have marginal distribution Poisson or Skellam. This new specification allows to incorporate relevant information about the nature of the correlations between all the components. In addition, we present some properties of this probability distribution function. Unlike the multivariate Poisson distribution initially introduced, this generalization enables to handle both positive and negative correlations. A simulation study illustrates the estimation in the two-dimensional case. The results obtained by Bayesian methods via Monte Carlo Markov chain (MCMC) suggest a fairly low relative bias of less than 5% for the regression coefficients of the mean. However, those of the covariance term seem a bit more volatile. Later, the chapter 4 presents an extension of the multivariate Poisson regression with random effects having a gamma density. Indeed, aware that the abundance data of species have a high dispersion, which would make misleading estimators and standard deviations, we introduce an approach based on integration by Monte Carlo sampling. The approach remains the same as in the previous chapter. Indeed, the objective is to simulate independent latent variables to transform the multivariate problem estimation in many generalized linear mixed models (GLMM) with conventional gamma random effects density. While the assumption of knowledge a priori dispersion parameters seems too strong and not realistic, a sensitivity analysis based on a measure of goodness of fit is used to demonstrate the robustness of the method. Finally, in the last chapter, we focus on the definition and construction of a measure of concordance or a correlation measure for some zeros augmented count data with Gaussian copula models. In contrast to Kendall's tau whose values lie in an interval whose bounds depend on the frequency of ties observations, this measure has the advantage of taking its values on the interval (-1, 1). Originally introduced to model the correlations between continuous variables, its extension to the discrete case implies certain restrictions and its values are no longer in the entire interval (-1,1) but only on a subset. Indeed, the new measure could be interpreted as the correlation between continuous random variables before being transformed to discrete variables considered as our discrete non negative observations. Two methods of estimation based on integration via Gaussian quadrature and maximum likelihood are presented. Some simulation studies show the robustness and the limits of our approach.