On Bayesian estimation of spatial and dynamic count models using data augmentation techniques : application to road safety management
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Over the past several years, roadway safety management has evolved into data-driven or evidence-based science. The corner stone of a data-driven roadway safety management is the knowledge about useful patterns in the complex crash data. Crash data is often difficult to model with several confounding factors and discrete target variables such as crash counts or crash severity. The major goal of this dissertation was to contribute to the methodological realm of roadway safety management. The research objectives are in two folds: 1) to develop state-of-the-art model specifications for modeling crash data, and 2) to develop a probabilistic model-based site ranking framework. This research addresses methodological issues in crash frequency modeling such as unobserved heterogeneity, spatial correlation, and temporal patterns. Two novel specifications were developed to address these methodological issues: 1) negative binomial spatial with random parameters (NBSRP) modeled as multi-variate normal finite mixture distribution; 2) negative binomial spatial model with dynamic parameters (NBSDP). The NBSRP with finite-mixture specification allows for identifying the underlying sub-groups of road segments, and for skewness and multi-modality in the underlying random parameter distribution. The NBSDP specification employs dynamic linear model (DLM) formulation of the discrete negative binomial count model by exploiting recently developed polya-gamma data-augmentation techniques. NBSDP model facilitates to investigate the evolution of the model parameters over the time and to make safety predictions for a future year. Both NBSRP and NBSDP models simultaneously accounts for potential spatial correlation of crash counts from neighboring road segments. Bayesian methods have been widely used for model building and recently gaining further popularity due to the availability of efficient algorithmic techniques for the parameter estimation. Computationally efficient Bayesian estimation frameworks that leverage recent advances in data augmentation techniques were developed in this research to estimate the proposed count specifications. Bayesian estimation methods also facilitate statistical inference on site ranks, thereby allowing for probabilistic ranking. A computationally efficient site ranking framework was developed incorporating the recent probabilistic ranking techniques towards the end of this dissertation. Overall, this dissertation demonstrates the feasibility of designing Bayesian modeling frameworks for probabilistic roadway safety management, which facilitate online learning. The research ideas presented in this dissertation may be extended to bigger networks to test the feasibility of developing a safety management framework that automatically learns from the latest crash data sources over the time.