Bayesian Modeling of Non-Stationary, Univariate, Spatial Data for the Earth Sciences

Techniques and Methods 7-C24
By:  and 



Some Earth science data, such as geochemical measurements of element concentrations, are non-stationary—the mean and the standard deviation vary spatially. It is important to estimate the spatial variations in both statistics because such information is indicative of geological and other Earth processes. To this end, an estimation method is formulated as a Bayesian hierarchical model. The method represents the spatially varying mean and the spatially varying standard deviation with basis functions; this formulation implicitly accounts for a spatially varying covariance function. A unique advantage of this method is that it can map the mean, the standard deviation, quantiles, and exceedance probabilities. The method is demonstrated by mapping titanium concentrations, which are measured in the coastal plain of the southeastern United States. Various checks demonstrate that the model fits the data and that the estimated statistics are geologically plausible.

Suggested Citation

Ellefsen, K.J., and Van Gosen, B.S., 2020, Bayesian modeling of non-stationary, univariate, spatial data for the Earth sciences: U.S. Geological Survey Techniques and Methods, book 7, chap. C24, 20 p.,

ISSN: 2328-7055 (online)

Table of Contents

  • Abstract
  • Introduction
  • Method
  • Demonstration of the Method
  • Discussion
  • Conclusions
  • Acknowledgments
  • Data, Software, and Reproducibility
  • References Cited
  • Appendix 1. Checks of Statistical Model
  • Appendix 2. Sensitivity Analysis
  • Appendix 3. Covariance Function
Publication type Report
Publication Subtype USGS Numbered Series
Title Bayesian modeling of non-stationary, univariate, spatial data for the Earth sciences
Series title Techniques and Methods
Series number 7-C24
DOI 10.3133/tm7C24
Year Published 2020
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Central Mineral and Environmental Resources Science Center, Crustal Geophysics and Geochemistry Science Center
Description Report: iii, 20 p.; Companion File
Online Only (Y/N) Y
Google Analytic Metrics Metrics page
Additional publication details