Probabilistic Tomography: A Pragmatic Bayesian Approach

Abstract:

'The future lies in uncertainty' (Spiegelhalter, Science, 345, 264, 2014), nothing could be more true for Earth Sciences. We are able to produce ever more sophisticated models but they can only inform us about the Earth in a meaningful way if we can assign uncertainties to the models. Bayesian inference is a natural choice for this task as it handles uncertainty in a natural way by explicitly modeling assumptions. Another desirable property is that Bayes' theorem contains Occam's razor implicitly. I will present our efforts over the that last 10 years to infer Earth properties using an approach we called probabilistic tomography. The word pragmatic has several meanings in this context. In more classical Bayesian inference problems, we usually prescribe subjective or informative priors. I will illustrate this by showing examples which employ the neighborhood algorithm (Sambridge, 1999) or a Metropolis rule (Mosegaard and Tarantola, 1995). Recently we started to use neural networks to parametrize the posterior. In our implementation, we do not sample the posterior directly, but make predictions on some properties of the posterior. The interpretation of the uncertainty is therefore slightly different, but the method informs us on the information gain with respect to the prior. I will show examples on source and structural inversions using so-called mixture density networks.