Most scholars encounter Bayesian statistics after learning classical, or Frequentist, statistics. As a result, Bayesian concepts and models are nearly always explained using Frequentist language. This can result in lasting confusion about the Bayesian approach, even among those who use it routinely. To advance this argument, I examine two cases of Frequentist language in widespread use in Bayesian statistics and reexplain the underlying concepts using new terms. The first case is the replacement of Frequentist "parameters" and "data" with Bayesian "variables". The second case is the replacement of both "likelihood" and "prior" with a unitary Bayesian concept. It is probably too late to change statistical terminology, but appreciating the friction created by using Frequentist terms in Bayesian contexts can help to avoid mistakes in both design and interpretation.

This was recorded as part of the TALMO meeting on Teaching Bayesian Methods.
More information and slides, etc, can be found at http://talmo.uk/2024/teachingbayesian...