Mean and Variance

Values based on small populations are corrected to be near the global or the local mean in the empirical Bayesian smoother. SpaceStat calculates the global and local sample means and variances as shown below.

The population-weighted mean, r , is the sum of the rate times the population for each location, divided by the total population-at-risk. The local mean (with the i subscript) uses a spatial weights term, wij. This spatial weights set is binary, with 1 for all neighbors (including ego, so a location is included in the local mean surrounding it) and 0 for all non-neighbors.

The shrinkage factor also uses the weighted sample variance. The sample variance is the population multiplied by the squared difference of the rate for a location from the mean rate, divided by the total population. Again, the local sample variance uses a spatial weights set to calculate a variance for only neighboring locations.