Searches for new physics are usually summarized by exclusion plots. After an overview of popular techniques at the LHC, we introduce a new way to present results from experimental searches for new physics — the Bayes factor surface [2401.11710]. Bayes factor surfaces indicate the strength of evidence for or against models relative to the background only model in terms of the phenomenological parameters that they predict. We discuss their relative strengths and weaknesses, and whether they could play a role in the presentation of scientific results at the CEPC.