Essay on Bayes

It has been said, fairly plausibly, that "Bayesian inference is one of the most widely known eponyms in all of science". But unlike common scientific eponyms, it is by no means clear exactly what "Bayesian" means, and what it has to do with Bayes. "Bayesian", and the dozen or so words and phrases which are usually associated with it, seem to be more like unspecific words of the English language, deployed by an author as he wishes, rather than fixed technical terms. The obscurity of the language, relative to the precise meanings associated with, say, Newton's laws or Heisenberg's uncertainty principle, is matched by the obscurity of the history - the virtually unknown Bayes, the posthumous paper, the impenetrable and incoherent style, the muddled logic, the virtual silence on his work for 200 years, the sudden emergence in the last several decades, not of new knowledge, but of new Bayesian additions to the vocabulary. This note surveys the notions and the history. It concludes that the Bayesian vocabulary is vague and pretentious, and serves no useful purpose.