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Techniques and Methods 7—C9

Groundwater Resources Program
Global Change Research and Development

Approaches in Highly Parameterized Inversion: bgaPEST, a Bayesian Geostatistical Approach Implementation With PEST—Documentation and Instructions

By Michael N. Fienen, Marco D’Oria, John E. Doherty, and Randall J. Hunt

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The application bgaPEST is a highly parameterized inversion software package implementing the Bayesian Geostatistical Approach in a framework compatible with the parameter estimation suite PEST. Highly parameterized inversion refers to cases in which parameters are distributed in space or time and are correlated with one another. The Bayesian aspect of bgaPEST is related to Bayesian probability theory in which prior information about parameters is formally revised on the basis of the calibration dataset used for the inversion. Conceptually, this approach formalizes the conditionality of estimated parameters on the specific data and model available. The geostatistical component of the method refers to the way in which prior information about the parameters is used. A geostatistical autocorrelation function is used to enforce structure on the parameters to avoid overfitting and unrealistic results. Bayesian Geostatistical Approach is designed to provide the smoothest solution that is consistent with the data. Optionally, users can specify a level of fit or estimate a balance between fit and model complexity informed by the data. Groundwater and surface-water applications are used as examples in this text, but the possible uses of bgaPEST extend to any distributed parameter applications.

First posted January 4, 2013

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Suggested citation:

Fienen, M.N., D’Oria, Marco, Doherty, J.E., and Hunt, R.J., 2013, Approaches in highly parameterized inversion: bgaPEST, a Bayesian geostatistical approach implementation with PEST—Documentation and instructions: U.S. Geological Survey Techniques and Methods, book 7, section C9 , 86 p., available only at




The Bayesian Geostatistical Approach

Overview of bgaPEST

Running bgaPEST

Suggestions and Guidelines for Initial Use

Limitations of bgaPEST Version 1.0


References Cited

Appendix 1: Input Instructions

Appendix 2: Quick Start Instructions

Appendix 3: Details of the Method

Appendix 4: Parallel Implementation of Jacobian Calculations

Appendix 5: Single-Layer Example Application

Appendix 6: Three-Layer Example Application

Appendix 7: Reverse Flood Routing Example Application

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