As a rather short (9 pages) introduction to Bayesian inference, I remember greatly appreciating an extract from the book "Information Theory, Inference, and Learning Algorithms" by David MacKay.<p>The relevant part is on PDF pages 469 to 477 here: <<a href="http://www.inference.phy.cam.ac.uk/itprnn/book.pdf>" rel="nofollow">http://www.inference.phy.cam.ac.uk/itprnn/book.pdf></a>;<p>It explains how Bayesian inference works (which is intuitive and not strange at all) and gives examples of absurdities that comes upon you when you don't do it this way.<p>Highlights:<p>• "Let me through, I’m a Bayesian" (When analysing the effectivness of a vaccine)<p>• "I have no problem with the idea that there is only one answer to a well-posed problem" (In response to sampling theorists wide selection of ad hoc procedures)