krigingbased

Kriging-based methods, sometimes referred to as krigingbased, are a family of geostatistical interpolation techniques that estimate the value of a spatially distributed variable at unobserved locations from observed measurements, using spatial autocorrelation described by a variogram or covariance function. The approach, named after Danie Krige and formalized by Georges Matheron, yields the best linear unbiased predictor under specified statistical assumptions and provides a kriging variance as a measure of prediction uncertainty.

Variants of kriging differ in how the mean structure is treated. Ordinary kriging assumes an unknown constant mean, simple kriging uses a known mean, and universal kriging allows a deterministic trend or drift. Cokriging extends the framework to incorporate secondary variables that correlate with the primary variable. Other forms include indicator kriging for categorical data and probabilistic or Bayesian kriging for distributional predictions. Localized or block kriging can produce estimates over neighborhoods or blocks rather than at a single point.

The typical workflow involves data quality control, exploratory data analysis, variogram or covariance estimation, variogram model fitting, solving the kriging system to obtain weights, and generating predictions with associated prediction variances. Validation is commonly performed via cross-validation or hold-out testing to assess predictive performance and model adequacy.

Applications of kriging-based methods span mining and mineral exploration, environmental monitoring, groundwater and hydrology, agriculture, meteorology, air and soil quality mapping, and land-use planning. Advantages include optimal linear estimation under stationarity assumptions, natural quantification of prediction uncertainty, and flexibility to handle irregular sampling and multiple data sources. Limitations include sensitivity to variogram choice, assumptions about stationarity, computational cost for large datasets, and potential bias from poorly modeled trends or outliers.