Spatial Statistics
Definition
Spatial statistics encompass descriptive and inferential methods tailored to spatial data’s unique properties—autocorrelation, nonstationarity, anisotropy, and boundary effects. They include point pattern analysis, spatial autocorrelation metrics, geostatistics (variograms, kriging), spatial regression, and Bayesian hierarchical models that share strength across neighbors. Key to spatial statistics is explicit modeling of spatial structure rather than pretending observations are independent.
Application
Applications span epidemiology, criminology, ecology, market analysis, agriculture, and environmental risk assessment. Spatial statistics power disease surveillance, precision agriculture prescriptions, habitat prediction, and policy evaluation where location matters.
FAQ
Why is spatial dependence both a challenge and an opportunity?
It violates i.i.d. assumptions but also provides information to improve estimates via borrowing strength from neighbors, reducing noise in sparse data.
How do Bayesian approaches benefit spatial analysis?
They integrate prior knowledge, propagate uncertainty, and naturally accommodate hierarchical spatial structures (e.g., neighborhoods within cities).
What’s the difference between first- and second-order effects?
First-order effects are broad trends (e.g., urban-rural gradient), while second-order effects describe interaction between points (clustering beyond the trend).
How should multiple testing be handled when scanning for hotspots?
Adjust p-values or use false discovery rate control to avoid spurious clusters when many locations are tested.