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In this paper, we aim at developing new methods to join machine learning techniques and macroscopic differential models for vehicular traffic estimation and forecast. It is well known that data-driven and model-driven approaches have…
In this chapter, we address the challenge of exploring the posterior distributions of Bayesian inverse problems with computationally intensive forward models. We consider various multivariate proposal distributions, and compare them with…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
We propose a generative multivariate posterior sampler via flow matching. It offers a simple training objective, and does not require access to likelihood evaluation. The method learns a dynamic, block-triangular velocity field in the joint…
We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a solute), a common experimental approach to…
Transportation departments take actions to manage traffic flow and reduce travel times based on estimated current and projected traffic conditions. Travel time estimates and forecasts require information on traffic density which are…
A classic network tomography problem is estimation of properties of the distribution of route traffic volumes based on counts taken on the network links. We consider inference for a general class of models for integer-valued traffic. Model…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
Modeling the relationship between vehicle speed and density on the road is a fundamental problem in traffic flow theory. Recent research found that using the least-squares (LS) method to calibrate single-regime speed-density models is…
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…
Modeling complex conditional distributions is critical in a variety of settings. Despite a long tradition of research into conditional density estimation, current methods employ either simple parametric forms or are difficult to learn in…
Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this…
The fundamental relationship of traffic flow is empirically estimated by fitting a regression curve to a cloud of observations of traffic variables. Such estimates, however, may suffer from the confounding/endogeneity bias due to omitted…
Normalizing flows can generate complex target distributions and thus show promise in many applications in Bayesian statistics as an alternative or complement to MCMC for sampling posteriors. Since no data set from the target posterior…
In this paper, a useful reinterpretation of the city as a porous medium justifies the application of well-known models on fluid dynamics to develop a multi-model study of urban air pollution due to traffic flow in a large city. Thus, to…
This paper offers an integrative data-driven physics-inspired approach to model and control traffic congestion in a resilient and efficient manner. While existing physics-based approaches commonly assign density and flow traffic states by…
Autoencoders gained popularity in the deep learning revolution given their ability to compress data and provide dimensionality reduction. Although prominent deep learning methods have been used to enhance autoencoders, the need to provide…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…