There is a paper (with discussion) on Statistical Science 2009, Vol. 24, No. 2 about Harold Jeffreys’ “Theory of Probability” book, which is one the foundations of Bayesian Statistics. The Institute of Mathematical Statistics (responsible for Statistical Science) encourages the deposit of the preprint-formatted articles in arxiv, thus providing us with the advantages from both publishing worlds: broad sharing of knowledge provided by the open repository and the quality of the academic peer-review. Here are the articles, with brief quotations from the abstracts or first paragraphs:
Published exactly seventy years ago, Jeffreys’s Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes school. In particular, its advances on the derivation of noninformative priors as well as on the scaling of Bayes factors have had a lasting impact on the field. However, the book reflects the characteristics of the time, especially in terms of mathematical rigor. In this paper we point out the fundamental aspects of this reference work, especially the thorough coverage of testing problems and the construction of both estimation and testing noninformative priors based on functional divergences. Our major aim here is to help modern readers in navigating in this difficult text and in concentrating on passages that are still relevant today.
The authors provide an authoritative lecture guide of Theory of Probability, where they clearly state that the more useful material today is that contained in Chapters 3 and 5, which respectively deal with estimation, and hypothesis testing. We argue that, from a contemporary viewpoint, the impact of Jeffreys proposals on those two problems is rather different, and we describe what we perceive to be the state of the question nowadays, suggesting that Jeffreys’s dramatically different treatment is not necessary, and that a joint objective approach to those two problems is indeed possible.
(…) In this brief discussion I will argue the following: (1) in thinking about prior distributions, we should go beyond Jeffreys’s principles and move toward weakly informative priors; (2) it is natural for those of us who work in social and computational sciences to favor complex models, contra Jeffreys’s preference for simplicity; and (3) a key generalization of Jeffreys’s ideas is to explicitly include model checking in the process of data analysis.
Theory of Probability is distinguished by several high-level philosophical attitudes, some stressed by Jeffreys, some implicit. By reviewing these we may recognize the importance in this work in the historical development of statistics.
I was taught by Harold Jeffreys, having attended his postgraduate lectures at Cambridge in the academic year 19461947, and also knew him when I joined the Faculty there. I thought I appreciated the Theory of Probability rather well, so was astonished to read this splendid paper, which so successfully sheds new light on the book by placing it in the context of recent developments.
I have always felt very guilty about Harold Jeffreys’s Theory of Probability (referred to as ToP, hereafter). I take seriously George Barnard’s injunction (Barnard, 1996) to have some familiarity with the four great systems of inference. I also consider it a duty and generally find it a pleasure to read the classics, but I find Jeffreys much harder going than Fisher, Neyman and Pearson fils or De Finetti. So I was intrigued to learn that Christian Robert and colleagues had produced an extensive chapter by chapter commentary on Jeffreys, honored to be invited to comment but apprehensive at the task.
The authors are to be congratulated for their deep appreciation of Jeffreys’s famous book, Theory of Probability, and their very impressive, knowledgeable consideration of its contents, chapter by chapter. Many will benefit from their analyses of topics in Jeffreys’s book. As they state in their abstract, “Our major aim here is to help modern readers in navigating this difficult text and in concentrating on passages that are still relevant today.” From what follows, it might have been more accurate to use the phrase, “modern well-informed Bayesian statisticians” rather than “modern readers” since the authors’ discussions assume a rather advanced knowledge of modern Bayesian statistics.
We are grateful to all discussants of our re-visitation for their strong support in our enterprise and for their overall agreement with our perspective. Further discussions with them and other leading statisticians showed that the legacy of Theory of Probability is alive and lasting.