PRACTICAL INVESTIGATIONS ON BAYESIAN INVERSE PROBLEMS

Inverse problems make up a challenging and practically important class of inference problems. Classical methods provide point estimates and confidence intervals which are asymptotically justified. As the computational power increased, however, ractitioners and researchers looked for better uncertainty quantification. The usual asymptotic confidence intervals gave way to full distributions using the Bayesian approach. This approach to inverse problems, while providing a full posterior distribution instead of a single point estimate as its answer, is also computationally much more expensive. Our contributions are two-fold. We present a novel adaptive sequential Monte Carlo method and its application to the groundwater-flow problem. Here, we observe significant time-savings compared to previous SMC approaches. We also observe, however, that this method is still too slow to be used in practice. Therefore, next, we turn our attention to multi-resolution (also known as multi-level) methods. We describe our implementation of this idea and show the match of experimental results to the predictions of asymptotic theory. This approach is promising for practical uncertainty quantification applications.

Author dc:creator

• MUZAFFER EGE ALPER

• Inverse Problems, Sequential Monte Carlo, Bayesian Inference, Computational Statistics, Adaptive Monte Carlo, Multilevel Monte Carlo