Most of us are aware from the news -- and from our daily use of internet platforms such as Google and Facebook -- how rapidly data science technology is moving forward. Physical scientists are also interested in harnessing the power of these new tools, but most applications have been limited to 'big data' methods, in which large amounts of experimental and simulation data is mined for clues regarding new materials, processes and reactions. This presentation will show how data science methods and sophisticated models can be used as advanced characterization tools in high-temperature electrochemistry. In particular, the power of model-based Bayesian methods will be demonstrated: relatively small amounts of data yield surprisingly large amounts of information about electrochemical processes. The primary example discussed will be oxygen reduction on porous Sr-doped lanthanum manganate solid oxide fuel cell cathodes, in which impedance data yields accurate measurements of the active width and the distribution of current among bulk and triple-phase boundary pathways.