Though lots has been written about Bayes, I wanted to convey to a lay audience what he achieved and why it’s so important now. Here is an attempt at a set of “footnotes” for anyone who wants to follow up:
The historical background is explained in:
- John Earman, Bayes or Bust (MIT Press)
- Edwin T. Jaynes, Probability Theory: the logic of science (Cambridge University Press) and his other writings.
The Jaynes book suggests some of the applications of Bayesianism that I mention, including radio astronomy. It was my own idea to include flirting as an example of a reverse inference problem: I’m sure people don’t usually think of it that way.
“Is Bayesianism just common sense…?” For examples of how medical or other decisions go wrong because people don’t think in a Bayesian way, an accessible introduction is Stuart Sutherland, Irrationality (Penguin paperback, reissued by Pinter & Martin). Similar material is covered in Chapter 12 of Scott Plous’ The Psychology of Judgement and Decision Making (McGraw-Hill). These authors in turn, are digesting the work of Amos Tversky, Daniel Kahneman and colleagues.
A full-on technical overview of Bayes’ theorem, why it should be taken seriously as a standard of reasoning, and how human judgements violate it, can be found in Jonathan Baron’s textbook Thinking and Deciding (Cambridge University Press).
According to my memory, although I can’t find the reference, the “Bayesian argument against torture” was proposed by the mathematician Robert Matthews.
“The training had absolutely no effect”: This remark conflates a number of different studies; I had to because of the limitations I was speaking under. Two papers reprinted in the book Judgment under uncertainty: Heuristics and biases describe how attempts to train people to be more Bayesian often made no difference: Alpert & Raiffa’s “A progress report on the training of probability assessors” and Lichtenstein, Fischhoff & Phillips’ “Calibration of Probabilities: The State of the Art.”