Standard Article

Empirical Bayes Methods


  1. Thomas A. Louis

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vae023

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Louis, T. A. 2006. Empirical Bayes Methods. Encyclopedia of Environmetrics. 2.

Author Information

  1. The RAND Corporation, VA, USA

Publication History

  1. Published Online: 15 SEP 2006


Statistical design, analysis, and reporting are fundamental to environmental research and assessment; to environmetrics. The variety and complexity of applications rapidly grows with a commensurate growth in statistical design and analysis. Environmental applications include all aspects of design, the analysis of spatially structured information (exposure, health outcomes, and demographics), nonlinear dose–response assays, interspecies extrapolation, placement of air or water monitoring stations, remote sensing, and gene–environment interactions. Analytic challenges include stabilizing estimates via statistical modeling and otherwise ‘borrowing information’, integrating information that is misaligned in space and time, dealing with missing data, accounting for measurement error in input information (e.g. exposures), missing data, causal modeling, addressing nonstandard goals and ensuring that statistical evaluations account for the dominant stochastic and modeling uncertainties. In addressing these and other challenges and goals, Bayes and empirical Bayes (EB) designs and analyses have proven valid, efficient, and informative. The beauty of the Bayesian approach is its ability to structure complicated assessments, guide development of appropriate statistical models and inferences, and produce summaries that properly account for uncertainties. Properly structured, these methods can produce objectively valid analyses, commonly more effective than traditional methods. When available, prior information can be integrated into the design and analysis. Computing innovations enable implementation of complex, relevant models and applications burgeon. This article outlines the Bayesian approach, traces the history of the EB approximation, gives a small sampling of environmetric applications and speculates on future developments.