Here is a book for Dennis Lindley on his 90th birthday. Dennis Lindley is a prominent Bayesian statistician who passed away on 14 December 2013. The book contains reminiscences from Dennis’s colleagues and friends. The book therefore provides a history (albeit in haphazard order) for the development of Bayesian statistics.

In addition, the reminiscences have some statistical gems. From Jim Berger’s, on multiple comparisons

I recall once being amazed in a discussion with Dennis to learn that multiple testing is not an issue with Bayesians; that it is automatically handled in the asssignment of prior probabilities to the hypotheses. I lately returned to this subject, upon realizing that this was necessarily true only for subjective Bayesian assignments of prior probabilities.

on Lindley’s Paradox

that, with a very large sample size, a Bayesian and a frequentist could be nearly certain about the truth of a hypothesis, but with the Bayesian being certain it is correct and the frequentist certain that it is wrong!

on credible intervals also being confidence intervals

I do enjoy showing that sound Bayesian procedures are also often optimal conditional frequentist procedures.

From Wesley Johnson on what it means to be Bayesian

During Dennis’s vist, he provided his defition of “Bayesian” at that time. As I recall it, it was : 1) Model all uncertainty with probability, and 2) Always obey the laws of probability. I still violate the first rule occasionally, by using improper priors.

From Tony O’Hagan on how some scientist interpret non-Bayesian analyses as Bayesian analyses

They [the scientists] automatically thought of a confidence interval as if it were a Bayesian credible interval, and they automatically factored in their prior knowledge. For instance, if I gave an estimate that was higher than they expected, on the basis of experience with their own experiments or the results of others, they would presume that the parameter was more likely to be below my estimate, rather than above.

From Christian Robert [with regard to the Lindley’s Paradox often called the Jeffrey-Lindley Paradox]

I thus remain convinced that the richest consequence of Jeffreys’s (1939) and Lindley’s (1957) exhibitions of this paradox is to highlight the difficulty in using improper or very vague priors in testing settings.

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15 January 2014