Techniques and Methods 7—C9
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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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 http://pubs.usgs.gov/tm/07/c09.
The Bayesian Geostatistical Approach
Overview of bgaPEST
Suggestions and Guidelines for Initial Use
Limitations of bgaPEST Version 1.0
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