Bayesian Statistics: An Introduction, 4th Edition

Preface to the First Edition

When I first learned a little statistics, I felt confused, and others I spoke to confessed that they had similar feelings. Not because the mathematics was difficult – most of that was a lot easier than pure mathematics – but because I found it difficult to follow the logic by which inferences were arrived at from data. It sounded as if the statement that a null hypothesis was rejected at the 5% level meant that there was only a 5% chance of that hypothesis was true, and yet the books warned me that this was not a permissible interpretation. Similarly, the statement that a 95% confidence interval for an unknown parameter ran from −2 to +2 sounded as if the parameter lay in that interval with 95% probability and yet I was warned that all I could say was that if I carried out similar procedures time after time then the unknown parameters would lie in the confidence intervals I constructed 95% of the time. It appeared that the books I looked at were not answering the questions that would naturally occur to a beginner, and that instead they answered some rather recondite questions which no one was likely to want to ask.

Subsequently, I discovered that the whole theory had been worked out in very considerable detail in such books as Lehmann (1986). But attempts such as those that Lehmann describes to put everything on a firm foundation raised even more questions. I gathered that the usual t test could be justified as a procedure that was `uniformly most ...