Trans-Conceptual Inversion: Bayesian Inference with Competing Assumptions

Over the past several decades Trans-dimensional Bayesian sampling has been widely applied in the geosciences. Most implementations have used the Reversible-jump Markov chain Monte Carlo (Rj-McMC) algorithm. This approach allows sampling across variably dimensioned model parameterizations and hierarchical noise models. Due to practical limitations Reversible-Jump is restricted to cases where the number of free parameters changes in a regular sequence, usually by addition or subtraction of a single variable. Furthermore, jumps between model dimensions rely on bespoke mathematical transformations that are only valid within a particular parametrization class. As a result, the range of model classes that can be practically considered is limited, and McMC balance conditions must be rederived for each class of problem. A framework for Trans-conceptual Bayesian sampling, which is a generalization of trans-dimensional sampling, is presented. Trans-C Bayesian inversion allows exploration across a finite, but arbitrary, set of conceptual models, i.e. ones where the number of variables, the type of model basis function, nature of the forward problem, and even assumptions on the class of measurement noise statistics, may all vary independently.

A key feature of the new framework is that it avoids parameter transformations and thereby lends itself to development of automatic McMC algorithms, i.e. where the details of the sampler do not require knowledge of the parameterization details. Algorithms implementing Bayesian conceptual model sampling are 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 where trans-D would be impractical, including asking the data to choose between competing forward models.