The Bayesian approach to inference from measurement data has the potential to provide highly reliable characterizations of flaw geometry by quantifying the confidence in the estimate results. The accuracy of these confidence estimates depends on the accuracy of the model for the measurement error. Eddy current measurements of electrically anisotropic metals, such as titanium, exhibit a phenomenon called “grain noise” in which the measurement error is spatially correlated even with no flaw present. We show that the most commonly used statistical model for the measurement error, which fails to account for this correlation, results in overconfidence in the flaw geometry estimates from eddy current data, thereby reducing the effectiveness of the Bayesian approach. We then describe a method of modeling the grain noise as a Gaussian process (GP) using spectral mixture kernels [1], a type of non-parametric model for the covariance kernel of a GP. This provides a broadly applicable, data-driven way of modeling correlation in measurement error. Our results show that incorporation of this noise model results in a more reliable estimate of the flaw and better agreement with the available validation data.