Probabilistic Interpolation
Content for Wednesday, October 29, 2025
Last class we talked about deterministic interpolation to fill in gaps in our data by leveraging the first law of geography (closer things should be similar). These approaches use the distance between observed data point and the observations themselves to calculate the values that occur between the obseved points. These approaches are deterministic - there is no uncertainty or stochasticity in the values they produce. Today, we’ll look at probabilistic approaches to interpolate missing values based on statistical models built on asssumptions about first- and second-order stationarity and estimates of covariance in our observed data.
Resources
Technical Details
Ch. 14: Kriging in from Paula Moraga’s new book Spatial Statistics for Data Science: Theory and Practice with
Rgives a little gentler introduction to spatial neighbors specifically in the context of statistical models.Chapter 12: Spatial Interpolation in Spatial Data Science by Edzer Pebesma and Roger Bivand provides some additional details for managing
gstatandsf, but relies onstarsa package we don’t use in this course.
Objectives
By the end of today you should be able to:
Differentiate deterministic from probabilistic interpolation
Recognize how first- and second-order properties relate to geostatistical interpolation
Define key components of a semi-variogram
Implement ordinary and universal krigging using
gstat,sf, andterra