Bayesian hierarchical spatial models: Implementing the Besag York Mollié model in stan - PubMed (original) (raw)

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

Mitzi Morris et al. Spat Spatiotemporal Epidemiol. 2019 Nov.

Abstract

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.

Copyright © 2019 Elsevier Ltd. All rights reserved.

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Figures

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Listing 1:

Program icar.stan

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Listing 2:

Program bym2.stan

Figure 1:

Figure 1:

Correlation Matrix for NYC Census Tracts ordered by Borough, Tract ID

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Figure 2:

Correlations Between Queens and Staten Island Census Tracts

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Figure 3:

School age pedestrians injured in traffic crashes, NYC 2005–2014

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Figure 4:

Histogram of school-age pedestrian injury counts per census tract, NYC 2005–2014

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Figure 5:

Posterior Predictive Check, density overlay

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Figure 6:

Posterior Predictive Check, test statistic

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Figure 7:

Per-tract injuries, actual counts vs. fitted BYM2 model estimates

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Figure 8:

Fitted BYM2 model estimated counts of school-age pedestrian crash injuries, 2005–2014

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