Bayesian non‐parametric spatial prior for traffic crash risk mapping: A case study of Victoria, Australia

Abstract

Summary We develop a Bayesian non‐parametric (BNP) model coupled with Markov random fields (MRFs) for risk mapping, to infer homogeneous spatial regions in terms of risks. In contrast to most existing methods, the proposed approach does not require an arbitrary commitment to a specified number of risk classes and determines their risk levels automatically. We consider settings in which the relevant information are counts and propose a so‐called BNP hidden MRF (BNP‐HMRF) model that is able to handle such data. The model inference is carried out using a variational Bayes expectation–maximisation algorithm and the approach is illustrated on traffic crash data in the state of Victoria, Australia. The obtained results corroborate well with the traffic safety literature. More generally, the model presented here for risk mapping offers an effective, convenient and fast way to conduct partition of spatially localised count data.

A Festschrift for Geoff McLachlan

“…Here, Durand et al . (2022) and Greve et al . (2022) provide Bayesian solutions for spatial regression data and vectorial data, respectively, whereas Hennig & Coretto (2022) consider an approach based on optimally tuned robust improper maximum likelihood estimation.…”

“…Other contributions to Theme (i) include the works of Durand et al . (2022), Greve et al . (2022), and Hennig & Coretto (2022), who each provide differing perspectives and solutions to the problem of clustering and mixture model estimation when the underlying number of clusters is unknown.…”

“…The works of Hui & Nghiem (2022) and Scrucca (2022) can also be viewed as contributions to this theme, with particular focus on the use of latent space representations via dimensionality reduction in order to facility better mixture-based clustering outcomes. Other contributions to Theme (i) include the works of Durand et al (2022), Greve et al (2022), andHennig &Coretto (2022), who each provide differing perspectives and solutions to the problem of clustering and mixture model estimation when the underlying number of clusters is unknown. Here, Durand et al (2022) and Greve et al (2022) provide Bayesian solutions for spatial regression data and vectorial data, respectively, whereas Hennig & Coretto (2022) consider an approach based on optimally tuned robust improper maximum likelihood estimation.…”