RSES Seminar Series 2024-11-21 Malcolm Sambridge (Australian National University)

When one of things you don’t know is the number of things that you don’t know.
Malcolm Sambridge (RSES) (Australian National University)
Abstract: Since its introduction in geophysics some twenty years ago, Trans-dimensional Bayesian Inference has become a popular approach for Bayesian sampling problems. It has been widely applied in solid Earth geophysics where the class of model representation of the subsurface; the number of free variables involved; or the level of data uncertainty is itself uncertain. The old adage goes that this approach is used ‘When one of the things that you don’t know is the number of things that you don’t know’.
There are, however, several limitations that have become evident over this time. One of which is that it’s really only practical when the number of free parameters in any problem differ in a (near) regular sequence between alternate models, usually by addition or subtraction of a single variable. Furthermore, implementation details are bespoke to each class of problem. As a result, implementations and software are only applicable within a limited class of problem. Change the physical set up, data type, or even conceptual assumptions about how to represent the Earth, and then the one usually has to start again from scratch.
A generalisation of Trans-D, which we call trans-conceptual, or Trans-C inversion is presented. Trans-C Bayesian sampling allows exploration across a finite, but arbitrary, set of situations where different conceptual assumptions are employed, i.e. ones where the number of variables, the type of model parameterisation, nature of the forward problem, and assumptions on the measurement noise statistics, may all vary independently. In contrast to trans-D the new framework lends itself to development of automatic implementations, i.e. where the details of the sampler do not require knowledge of the parameterization. Algorithms implementing Bayesian conceptual model sampling are presented and illustrated with examples drawn from geophysics, using real and synthetic data. Comparison with reversible-jump illustrates that Trans-C sampling produces statistically identical results for situations where the former is applicable, but also allows sampling in situations Trans-D would be impractical to implement, e.g. where the data is to be used to constrain an Earth model using a range of competing conceptual assumptions. Trans-C holds the promise that we can move beyond the situation where we base our inferences on a whole set of, possibly poorly justified or unverifiable, assumptions.