Estimation

A longstanding and important problem in geological mapping and modeling is the calculation of estimates at unsampled locations. Kriging is widely used in geostatistics for this purpose. The central idea is to calculate an estimate that minimizes the expected squared error between the unknown true value and the estimate. In general, all data that are related to the unsampled location should have an opportunity to influence the estimate.

A central feature of geostatistics from the early days in the 1960s is that estimation must consider a site-specific variogram model of spatial correlation that accounts for the spatial structure of the variable being estimated including anisotropy and other detailed features. Another central feature of estimation is that the estimates should be constructed with a clearly defined measure of optimality. In practice, an optimal estimate is one that minimizes the estimation variance. Lessons here are focused on the decisions required in the construction of optimal estimates.

Lessons

• Signed Distance Function Modeling with Multiple Categories
• Implicit Boundary Modeling with Radial Basis Functions
• Introduction to Choosing a Kriging Plan (see source code on GitHub)
• Kriging with Constraints
• Quantitative Kriging Neighborhood Analysis (QKNA)
• Choosing the Discretization Level for Block Property Estimation
• Collocated Cokriging (see source code on GitHub)
• Kriging Weights in the Presence of Redundant Data
• An Overview of Multiple Indicator Kriging

• Trend Modeling and Modeling with a Trend (see source code on GitHub)
• The Pairwise Relative Variogram (see source code on GitHub)
• Conditioning by Kriging
• Locally Varying Anisotropy
• The Sill of the Variogram
• The Decision of Stationarity
• Transforming a Variogram of Normal Scores to Original Units
• The Nugget Effect (see source code on GitHub)
• Change of Support and the Volume Variance Relation