  Density Functional Theory (DFT) calculations are being routinely used to
identify new material candidates that approach activity near fundamental limits
imposed by thermodynamics or scaling relations. DFT calculations have finite
uncertainty and this raises an issue related to the ability to delineate
materials that possess high activity. With the development of error estimation
capabilities in DFT, there is an urgent need to propagate uncertainty through
activity prediction models. In this work, we demonstrate a rigorous approach to
propagate uncertainty within thermodynamic activity models. This maps the
calculated activity into a probability distribution, and can be used to
calculate the expectation value of the distribution, termed as the expected
activity. We prove that the ability to distinguish materials increases with
reducing uncertainty. We define a quantity, prediction efficiency, which
provides a precise measure of the ability to distinguish the activity of
materials for a reaction scheme over an activity range. We demonstrate the
framework for 4 important electrochemical reactions, hydrogen evolution,
chlorine evolution, oxygen reduction and oxygen evolution. We argue that future
studies should utilize the expected activity and prediction efficiency to
improve the likelihood of identifying material candidates that can possess high
activity.
