Uncertainty in the transmitter position, theory error and insufficient model parameterization amongst various other factors can lead to significant correlated error in observed controlled source electromagnetic data. These errors come to light by an examination of the residuals after performing inversion. Since correlated error violates the assumption of independent data noise it can manifest in spurious structure in inverted models. We demonstrate this using both synthetic data and real data from Scarborough gas field, North West Australia. In this work we propose a method which uses a hierarchical Bayesian framework and reversible jump Markov chain Monte Carlo to account for correlated error. We find that this removes suspect structure from the inverted models and within reasonable prior bounds, provides information on the resolution of resistivity at depth.