Using Bayesian Statistics to Capture the Effects of Modelling Errors in Inverse Problems
- J. N. Carter
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When the parameters of a numerical model are adjusted, so that the predictions of the model match measurements from the real system, we need to take account of two sources of errors. These being measurement errors and modelling errors. Measurement errors are commonly considered, and a number of different approaches are in general usage, the most common being the weighted sum of squares method. In this paper the standard Bayesian equation, used for inverse problems, is reformulated so as to make it more intuitive to use. This allows the inclusion of both a modelling error and correlations between measurements to be carried out easily. The results are tested on a simple one-parameter numerical model and a cross-sectional model of a petroleum reservoir. In the first case the proposed error model appears to work well. In the second case it appears that the objective function is multimodal, leading to multiple acceptable solutions. The results of this paper are important to those whose numerical models are thought to contain significant modelling error. This encompasses many areas of modelling related to earth science and engineering.
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- Using Bayesian Statistics to Capture the Effects of Modelling Errors in Inverse Problems
Volume 36, Issue 2 , pp 187-216
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- sum of squares
- Bayesian analysis
- Industry Sectors
- J. N. Carter (1)
- Author Affiliations
- 1. Department of Earth Sciences and Engineering, Imperial College, London, SW7 2AZ, United Kingdom