Bayesian Markov-chain-Monte-Carlo (McMC) techniques are widely used in geophysics due to their ability to estimate multiple outcomes that enable uncertainty assessment. Standard McMC sampling methods, however, can become computationally intractable for high-dimensional problems. We present a Bayesian McMC framework that re-parameterizes the McMC procedure in terms of an optimal basis, thereby enabling a sparse representation of the desired features leading to dimensionality reduction. The approach also implicitly incorporates the physics of the underlying process. We demonstrate the performance of the algorithm on a synthetic example involving electrical resistivity imaging of unimodal and bimodal solute plumes. We show that Bayesian-McMC inversion can proceed in the reduced dimensional model space in order to make it tractable and produce physically realistic solute plumes.

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