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Table 2 Performance comparison of Bayesian and geostatistical estimators: mean error of prediction.

From: How does Poisson kriging compare to the popular BYM model for mapping disease risks?

Estimators Lung cancer Cervix cancer
Arithmetical average Average % best result Average % best result
Global Empirical Bayes -0.031 22 0.053 18
Local Empirical Bayes 0.012 14 0.006 28
BYM Model 0.010 12 0.006 16
Point Poisson kriging (adjacent counties) 0.009 14 0.019 22
ATA Poisson kriging (adjacent counties) 0.014 20 0.023 8
ATA Poisson kriging (32 neighbors) -0.001 18 0.040 8
Population-weighted average     
Global Empirical Bayes -0.026 26 0.012 32
Local Empirical Bayes -0.011 22 0.001 32
BYM Model -0.009 18 0.001 12
Point Poisson kriging (adjacent counties) -0.011 16 0.001 10
ATA Poisson kriging (adjacent counties) -0.011 4 0.001 8
ATA Poisson kriging (32 neighbors) -0.016 14 0.002 6
  1. Results obtained on average (arithmetical and population-weighted) over 50 realizations generated for Regions 1 and 2. Poisson kriging was conducted using either adjacent counties (same neighbors as BYM model) or the 32 closest counties in terms of distance between population-weighted centroids. ATA kriging accounts for the shape and size of the counties in the analysis. Straightforward empirical Bayesian smoothers were also applied. Bold numbers refer to best performances. The second column gives the percentage of realizations where the particular method yields the smallest prediction error.