501. Bayesian inference, Gibbs sampler and uncertainty estimation in nonlinear geophysical inversion
- Author
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Paul L. Stoffa and Mrinal K. Sen
- Subjects
Function (mathematics) ,Inverse problem ,Bayesian inference ,Space (mathematics) ,Statistics::Computation ,Nonlinear system ,symbols.namesake ,Bayes' theorem ,symbols ,Applied mathematics ,Geomorphology ,Geology ,Importance sampling ,Gibbs sampling - Abstract
The Bayes or the Tarantola-Vallette formulation of the geophysical inverse problem describes the solution of the inverse problem as the a posteriori probability density (PPD) function in model space. Since the complete description of the PPD is impossible in the highly multidimensional model space of geophysical applications, several measures such as the highest posterior density regions, marginal PPD and several orders of moments are often used to describe the solutions. Calculation of such quantities requires evaluation of multi-dimensional integrale. A faster alternative to enumeration and blind Monte-Carlo integration is importance sampling which may be useful in several applications. Importance sampling can be carried out most efficiently by a Gibbs sampler (Geman and Geman, 1984). We introduce here a new method called the parallel Gibbs sampler (PGS) based on genetic algorithms and show that the results from the two samplers are nearly identical.
- Published
- 1994
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