Bayesian hierarchical spatial models: Implementing the Besag York Mollié model in stan
- Resource Type
- Authors
- Mitzi Morris; Charles DiMaggio; Stephen J. Mooney; Katherine Wheeler-Martin; Daniel Simpson; Andrew Gelman
- Source
- Spat Spatiotemporal Epidemiol
- Subject
- Spatial Analysis
Models, Statistical
Epidemiology
Computer science
Health, Toxicology and Mutagenesis
030231 tropical medicine
Geography, Planning and Development
Bayesian probability
Probabilistic logic
Accidents, Traffic
Bayes Theorem
Pedestrian
Census
Bayesian inference
Article
Besag york mollie
Social fragmentation
Hybrid Monte Carlo
03 medical and health sciences
0302 clinical medicine
Infectious Diseases
Statistics
Humans
New York City
030212 general & internal medicine
- Language
- ISSN
- 1877-5853
This report presents a new implementation of the Besag-York-Mollie (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.