Efficient probabilistic inversion using the rejection sampler-exemplified on airborne EM data

Probabilistic inversion methods, typically based on Markov chain Monte Carlo, exist that allow exploring the full uncertainty of geophysical inverse problems. The use of such methods is though limited by significant computational demands, and non-trivial analysis of the obtained set of dependent models. Here, a novel approach, for sampling the posterior distribution is suggested based on using pre-calculated lookup tables with the extended rejection sampler. The method is (1) fast, (2) generates independent realizations of the posterior, and (3) does not get stuck in local minima. It can be applied to any inverse problem (and sample an approximate posterior distribution) but is most promising applied to problems with informed prior information and/or localized inverse problems. The method is tested on the inversion of airborne electromagnetic data and shows an increase in the computational efficiency of many orders of magnitude as compared to using the extended Metropolis algorithm.

Automated summary

A new approach for sampling posterior distribution is proposed using pre-calculated lookup tables and extended rejection sampler, which is fast, generates independent realizations of the posterior, and does not get stuck in local minima. It can be applied to any inverse problem to sample an approximate posterior distribution, but is most promising for problems with informed prior information and/or localized inverse problems.