Bayesian hierarchical spatial models: Implementing the Besag York Mollié model in stan

Spat Spatiotemporal Epidemiol. 2019 Nov;31:100301. doi: 10.1016/j.sste.2019.100301. Epub 2019 Aug 12.


This report presents a new implementation of the Besag-York-Mollié (BYM) model in Stan, a probabilistic programming platform which does full Bayesian inference using Hamiltonian Monte Carlo (HMC). We review the spatial auto-correlation models used for areal data and disease risk mapping, and describe the corresponding Stan implementations. We also present a case study using Stan to fit a BYM model for motor vehicle crashes injuring school-age pedestrians in New York City from 2005 to 2014 localized to census tracts. Stan efficiently fit our multivariable BYM model having a large number of observations (n=2095 census tracts) with small outcome counts < 10 in the majority of tracts. Our findings reinforced that neighborhood income and social fragmentation are significant correlates of school-age pedestrian injuries. We also observed that nationally-available census tract estimates of commuting methods may serve as a useful indicator of underlying pedestrian densities.

Keywords: Bayesian inference; Besag-York-Mollié model; Intrinsic conditional auto-regressive model; Pedestrian injuries; Probabilistic programming; Stan.

MeSH terms

  • Accidents, Traffic / statistics & numerical data*
  • Bayes Theorem
  • Humans
  • Models, Statistical*
  • New York City
  • Spatial Analysis*