Spatial Statistics and Geostatistics for Actuaries

Spatial Data Types

Spatial statistics analyzes data with geographic coordinates. Three types of spatial data arise in actuarial work: point patterns (locations of claims or policyholders), geostatistical data (continuous measurements at sampled locations, like property values), and lattice/areal data (aggregated over regions, like county-level claim rates). Spatial autocorrelation means nearby observations are more similar than distant ones. Moran's I and Geary's C measure spatial autocorrelation. The variogram gamma(h) = 0.5*E[(Z(s+h) minus Z(s))^2] characterizes spatial dependence as a function of distance h.

Actuarial Applications

In insurance, spatial analysis supports territory rating by identifying geographic clusters of high or low loss costs. Kriging uses the variogram to interpolate values at unobserved locations, providing optimal predictions with quantified uncertainty. Spatial regression models account for geographic correlation that standard regression ignores. Catastrophe risk assessment uses spatial models to estimate losses from events affecting broad geographic areas. Exam MAS-I covers basic spatial concepts, variogram interpretation, and the rationale for spatial methods in actuarial applications.