Last week, Christian Robert and I separately reviewed Krzysztof Burdzy’s book, The Search for Certainty, which I characterized as a harmless if misleading discussion of the philosophy of probability. Burdzy sent us his reply, which I will post below, followed by my comments. I am omitting some parts of Burdzy’s comments that are specifc to Christian’s review and not of general interest.
Dear Professors Gelman and Robert,
First of all, thank you for reading my book. I will refer to [your] reviews as [CR] and [AG]. I will refer to my book as [KB]. Since I referred to the foundations of probability as “one of the greatest intellectual failures of the twentieth century”, I should not have expected an enthusiastic reaction from the community or probabilists, statisticians and philosophers. Hence, your criticism is not a great surprise for me. In this reply, I will try to avoid opinions, as much as it is possible in this area–we obviously have different opinions and we all expressed them in public. I will try focus on facts, because this may help the readers of your reviews and the readers of my book.
1. I witnessed the following event. Wilfrid Kendall was asked a question at the end of a talk at a conference. He said “My answer will be very aggressive. I totally agree with you.” (He followed with more substantial remarks). My reaction to your reviews will be very aggressive|I totally agree with you. Well, to be honest, I totally agree on one point: “[the book does not make] a significant contribution to the foundations of statistical inference in general and of Bayesian analysis in particular.” ([CR] p. 7). On page vii of [KB], I clearly state my three intellectual goals: (i) Criticism of von Mises and de Finetti, (ii) Presentation of my “scientific theory or probability”, and (iii) Education of scientists about philosophical theories of probability. The subtitle of [KB] (at least implicitly) indicates that the book is about the miscommunication between philosophers and scientists. On p. 199 of [KB] I say that it is not my ambition to reform statistics. I would have never stated my intellectual goals as a desire to make “a significant contribution to the foundations of statistical inference in general and of Bayesian analysis in particular.”
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5. On p. 6 of [CR], the following quote from [KB] is given: “subjective theory does not provide any justification for the use of the Bayes theorem”. A very similar quote appears in the second to last paragraph of [AG]. I find it amusing that [CR] calls my claim “rather nonsensical” while [AG] says “fine by me, but of course nothing new.” I can’t win–if my claim is true, I failed to notice that it was well known; if it is false, I failed to notice that it was nonsensical.
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8. On p. 3 of [CR] there is a remark on the “lack of involved examples”. I do not see how involved examples could have changed the perception of my book. I do not have any new frequency or Bayesian statistical methods to propose. I believe that all statisticians, probabilists and other scientists should use (L1)-(L5) to teach the basic principles of probability. Would involved examples make (L1)-(L5) more attractive to you?
9. On p. 6 of [CR] I am criticized for concentrating \on two very specific entries to frequentism and subjectivism, namely von Mises’ and de Finetti’s, respectively, while those are not your average statistician’s references.” I explain on p. 12 of [KB] why I chose the theories of von Mises and de Finetti. Let me repeat and rephrase my reasons. These two theories are more or less complete and more or less logically consistent philosophical theories created by people who are recognized by philosophers as the leading figures in frequency and subjective currents of philosophy of probability. De Finetti and von Mises wrote books that I could study and criticize. There is an implicit suggestion in [CR] that I have chosen the wrong theories to criticize and that statisticians apparently use other philosophical theories. As far as I can tell, statisticians have a multitude of philosophical opinions but that does not mean that these opinions add up to a logically consistent theory. If I ever want to criticize the Catholic theology, I will use the official Vatican doctrine as the target of my criticism. It is unquestionably true that the real religious beliefs of Catholics are quite often different from the Vatican doctrine, but the union of all beliefs of all Catholics does not add up to a logically consistent philosophy (as far as I can tell).
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My comments: I stand by my opinion that, from this statistician’s perspective, Burdzy’s book is unremarkable except in its insistence on its remarkability. I also continue to disagree with his statement that “standard textbooks on chemistry do not discuss subjectivity in their introductions, and so statistical textbooks need not to do that either”; yes, chemistry and statistics overlap–I’ve done some work on toxicology, myself–but overall I think the two fields can think about their textbooks independently. Regarding Burdzy’s point 9 above, he can feel free to criticize von Mises, de Finetti, or even Pope Benedict. None of this has any impact on my work but it could be of interest to others.
Finally, regarding point 5 above, let me emphasize that Christian Robert and I are two different people. in any case, I hope this discussion is helpful to somebody somewhere!