# ArcUserSummer 2014

Summer 2014

## A Little More about Two Geostatistical Methods

### Empirical Bayesian Kriging

Empirical Bayesian kriging (EBK) is a geostatistical interpolation method that automates the most difficult aspects of building a valid kriging model. Other kriging methods in the ArcGIS Geostatistical Analyst extension require manual adjustment of parameters to generate accurate results. However, EBK automatically calculates these parameters through a process of subsetting and simulations.

EBK also differs from other kriging methods by accounting for the error introduced by estimating the underlying semivariogram. Other kriging methods calculate the semivariogram from known data locations and use this single semivariogram to make predictions at unknown locations. This process implicitly assumes that the estimated semivariogram is the true semivariogram for the interpolation region. By not taking the uncertainty of semivariogram estimation into account, other kriging methods underestimate the standard errors of prediction.

For a detailed description of EBK, read "Empirical Bayesian Kriging Implemented in ArcGIS Geostatistical Analyst" by Konstantin Krivoruchko, published in the Fall 2012 issue of ArcUser.

### Kernel Smoothing

Kernel smoothing is a variant of local polynomial interpolation. It is equivalent to the universal kriging model when all spatial variation is described by the trend and the semivariogram model simply describes spatially uncorrelated measurement error (called the nugget effect in geostatistical literature). When barriers are present, the distance between points is calculated as the shortest sum of the series of lines that do not intersect the polylines.

No interpolation model can predict values at the unsampled locations without some error, whether small or large. Therefore, a good method should include a measure of prediction uncertainty so the quality of predictions can be evaluated. Kernel smoothing has a measure of prediction uncertainty, which is uncommon among deterministic interpolation methods.