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We propose a Stochastic MPC (SMPC) formulation for autonomous driving at traffic intersections which incorporates multi-modal predictions of surrounding vehicles for collision avoidance constraints. The multi-modal predictions are obtained…

Systems and Control · Electrical Eng. & Systems 2022-03-01 Siddharth H. Nair , Vijay Govindarajan , Theresa Lin , Chris Meissen , H. Eric Tseng , Francesco Borrelli

Latent Gaussian models are an extremely popular, flexible class of models. Bayesian inference for these models is, however, tricky and time consuming. Recently, Rue, Martino and Chopin introduced the Integrated Nested Laplace Approximation…

Computation · Statistics 2011-05-17 Daniel Simpson , Finn Lindgren , Håvard Rue

Bayesian hierarchical models with latent Gaussian layers have proven very flexible in capturing complex stochastic behavior and hierarchical structures in high-dimensional spatial and spatio-temporal data. Whereas simulation-based Bayesian…

Methodology · Statistics 2017-08-10 Thomas Opitz

Robust time series analysis is an important subject in statistical modeling. Models based on Gaussian distribution are sensitive to outliers, which may imply in a significant degradation in estimation performance as well as in prediction…

Traffic control optimization is a challenging task for various traffic centers around the world and the majority of existing approaches focus only on developing adaptive methods under normal (recurrent) traffic conditions. Optimizing the…

Machine Learning · Computer Science 2021-03-16 Tuo Mao , Adriana-Simona Mihaita , Fang Chen , Hai L. Vu

Bayesian inference tasks continue to pose a computational challenge. This especially holds for spatial-temporal modeling where high-dimensional latent parameter spaces are ubiquitous. The methodology of integrated nested Laplace…

Computation · Statistics 2023-03-28 Lisa Gaedke-Merzhäuser , Elias Krainski , Radim Janalik , Håvard Rue , Olaf Schenk

To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge about unobserved covariates can be incorporated in the prior distributions. However, given the analytic…

Methodology · Statistics 2013-08-19 Stefanie Muff , Andrea Riebler , Havard Rue , Philippe Saner , Leonhard Held

Motion prediction for intelligent vehicles typically focuses on estimating the most probable future evolutions of a traffic scenario. Estimating the gap acceptance, i.e., whether a vehicle merges or crosses before another vehicle with the…

Robotics · Computer Science 2024-09-18 Max Bastian Mertens , Jona Ruof , Jan Strohbeck , Michael Buchholz

Latent Gaussian models (LGMs) are a popular class of Bayesian hierarchical models that include Gaussian processes, as well as certain spatial models and mixed-effect models. Efficient Bayesian inference of LGMs often requires marginalizing…

Machine Learning · Statistics 2026-05-21 Jinlin Lai , Charles C. Margossian , Daniel R. Sheldon

The key operation in Bayesian inference, is to compute high-dimensional integrals. An old approximate technique is the Laplace method or approximation, which dates back to Pierre- Simon Laplace (1774). This simple idea approximates the…

We introduce a new copula-based correction for generalized linear mixed models (GLMMs) within the integrated nested Laplace approximation (INLA) approach for approximate Bayesian inference for latent Gaussian models. While INLA is usually…

Computation · Statistics 2015-12-16 Egil Ferkingstad , Håvard Rue

Autonomous agents must be able to safely interact with other vehicles to integrate into urban environments. The safety of these agents is dependent on their ability to predict collisions with other vehicles' future trajectories for…

Robotics · Computer Science 2020-02-07 Andrew Patterson , Aditya Gahlawat , Naira Hovakimyan

Integrated Nested Laplace Approximation provides a fast and effective method for marginal inference on Bayesian hierarchical models. This methodology has been implemented in the R-INLA package which permits INLA to be used from within R…

Computation · Statistics 2021-06-01 Virgilio Gomez-Rubio , Roger S. Bivand , Håvard Rue

In this paper, we investigate traffic signal control in a network of interconnected intersections, aiming to balance lane-level vehicle densities through optimal green-time allocation. We develop a two-lane traffic flow model that…

Systems and Control · Electrical Eng. & Systems 2025-12-09 Xinfeng Ru , Ting Bai , Weiguo Xia , Andreas A. Malikopoulos

Traffic flow forecasting, especially the short-term case, is an important topic in intelligent transportation systems (ITS). This paper does a lot of research on network-scale modeling and forecasting of short-term traffic flows. Firstly,…

Machine Learning · Computer Science 2018-01-03 Shiliang Sun , Rongqing Huang , Ya Gao

The integrated nested Laplace approximations (INLA) method has become a widely utilized tool for researchers and practitioners seeking to perform approximate Bayesian inference across various fields of application. To address the growing…

Computation · Statistics 2023-11-15 Esmail Abdul-Fattah , Janet Van Niekerk , Haavard Rue

As a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we explore empirically the sampling challenges this approach offers which have to do with the strong correlations and multi-modality of the…

Computation · Statistics 2021-08-11 Jeremie Coullon , Yvo Pokern

Misclassified variables used in regression models, either as a covariate or as the response, may lead to biased estimators and incorrect inference. Even though Bayesian models to adjust for misclassification error exist, it has not been…

Methodology · Statistics 2024-11-26 Emma Skarstein , Leonardo Soares Bastos , Håvard Rue , Stefanie Muff

Accurate traffic prediction plays a vital role in intelligent transportation systems by enabling efficient routing, congestion mitigation, and proactive traffic control. However, forecasting is challenging due to the combined effects of…

Machine Learning · Computer Science 2025-07-08 Mohamed Hamad , Mohamed Mabrok , Nizar Zorba

This study proposes a deep generative adversarial architecture (GAA) for network-wide spatial-temporal traffic state estimation. The GAA is able to combine traffic flow theory with neural networks and thus improve the accuracy of traffic…

Signal Processing · Electrical Eng. & Systems 2018-01-12 Yunyi Liang , Zhiyong Cui , Yu Tian , Huimiao Chen , Yinhai Wang