Spatial interpolation (kriging), explained for epidemiologists

BioMedware · 8 min read

You have measurements at a handful of places and need an estimate everywhere else. Kriging gives you that estimate, and it also tells you how far to trust it.

Nearby things are more alike

Kriging starts from a simple observation: samples close together tend to have similar values. The variogram measures how that similarity decays with distance. Its three parameters have plain meanings. The nugget is variation you see even at zero distance, from measurement error or very local effects. The sill is the total variance. The range is the distance beyond which samples stop telling you anything about each other.

A variogram chart for soil organic carbon: blue experimental points rising from a semivariance near 0.5 to a plateau just above 1.1 over about 570 m, with the fitted model curve through them and a dashed line for the sample variance. — Figure 1. Experimental semivariance (points) and the fitted Cubic model (line) for soil organic carbon across one Ontario field, from the Soil organic carbon sample. The nugget is about 0.52 and the sill about 1.17.

From weights to a surface

For each location without a sample, kriging finds the weighted average of nearby samples that is unbiased and has the smallest expected error, given the variogram. Closer and less redundant samples get more weight. Repeat that across a grid and you have a continuous surface.

Try it in Vesta OnlineOpen the sample project “Well-water arsenic”, then ask the Advisor: “Fit a variogram and krige arsenic across the county.”

Report the uncertainty too

Every kriged estimate comes with a kriging variance. Map it next to the estimate: areas far from samples will show high variance, and that is where to be careful with conclusions, or where to sample next.

Spatial interpolation (kriging), explained for epidemiologists

Nearby things are more alike

From weights to a surface

Report the uncertainty too

Run kriging without writing code.