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A Bayesian Statistical Approach for Inference on Static Origin–Destination Matrices in Transportation Studies

Summary: [This abstract is based on the authors' abstract.] This article address the problem of static origin–destination matrix reconstruction for transportation systems. This problem is similar to missing data estimation in contingency tables where the observed data, the table margins, give little information to drive the inference. In this article, the author incorporates other sources of data that are common in transportation studies — seed matrices and trip cost distributions — to develop a novel class of hierarchical Bayesian models that provide better estimators. Moreover, classical solutions from growth factor, gravity, and maximum entropy models are identified as specific estimators under the proposed models. The article shows, however, that each of these solutions accounts for a small fraction of the posterior probability mass in the ensemble, and so it is contended that the uncertainty in the inference should be propagated to later analyses or next-stage models. Markov chain Monte Carlo sampling schemes are devised to obtain more robust estimators and perform other types of inferences. The article presents a synthetic example and a real-world case study in the city of Warwick, Australia, showcasing the proposed models and highlighting how other sources of data can be incorporated in the model to conduct inference in a principled, nonheuristic way.

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  • Topics: Sampling
  • Keywords: Case study, Transportation Industry, Australia, Bayesian methods, Matrix, Hierarchical systems, Markov chains, Monte Carlo methods, Uncertainty, Inference procedures, Constraints, Sampling
  • Author: Carvalho, Luis;
  • Journal: Technometrics