Free Stats Textbook: Principles of Uncertainty

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Joseph Kadane, emeritus at Carnegie Mellon, released his new statistics textbook Principles of Uncertainty as a free pdf. The book is written from a Bayesian perspective, covering basic probability, decision theory, conjugate distribution analysis, hierarchical modeling, MCMC simulation, and game theory. The focus is mathematical, but computation with R is touched on. A solid understanding of calculus seems sufficient to use the book. Curiously, the author devotes a fair number of pages to developing the McShane integral, which is equivalent to Lebesgue integration on the real line. There are lots of other unusual topics you don’t normally see in an intermediate statistics textbook.

Having came across this today, I can’t say whether it is actually very good or not, but the range of topics seems perfectly suited to Less Wrong readers.

[Cyan]

Before we begin, I emphasize that the answers you give to the questions I ask you about your uncertainty are yours alone, and need not be the same as what someone else would say, even someone with the same information as you have, and facing the same decisions.

- Principles of Uncertainty, page 1, emphasis added

I attended a statistics conference in January at which Jay Kadane (in attendence) was described as one of the last still-living original subjective Bayesians. I’m not sure how many currently practicing Bayesian hold to this line. For example, Brad Carlin, an organizer of said conference, mentioned Kadane’s philosophical stance in this comment about a book he (Carlin) wrote:

… Don [Berry, who got his Ph.D. under Kadane] gave me some older “white papers” he’d written on this subject for introductory audiences, but never published. I took these and edited/​re-cut them into Chapter 1 and parts of Chapter 2… because these “white papers” were older, they reflected Don’s much more subjective Bayesian views of 10-15 years ago. I should have been more careful in editing out some of this stuff, because it’s not the way he or I or any “working Bayesian” thinks any more… But this point of view was still feasible back then; see e.g. Jay Kadane’s book for a purely subjective Bayes take (unsurprising given its author) on clinical trials.

Personally, I am of the Jaynesian school of thought which holds that if two agents have the same state of information, then they ought to assign the same probability distributions.

[beoShaffer]

I’ve been reading this. The explanations are good and the exercises are interesting, but I can’t find any form of solutions manual(if there is one please let me know). This is a big drawback if you want to use it for self/​independent study.

[snarles]

If only this book had some more examples of applications, it be a contender for ‘best introductory textbook for statistics’. As it stands, it makes a great complement to either Wasserman’s All of Statistics (filling in the Bayesian side of things) or Gelman, Carlin, Rubin, Stern’s Bayesian Data Analysis (filling in theoretical side of things.) There has been a huge need for a ‘Jaynes-lite’ which offers the philosophical grounding of P:tLoS sans its distracting (and now outdated) polemics.

[jsalvatier]

How does this compare to Data Analysis: A Bayesian Tutorial? In any case, you should post your suggestion in the Best Textbooks thread.

[snarles]

I haven’t looked through Silva. Kadane does have the advantage of being free to access, however!

[Antisuji]

I’ll second this question. I just started going through Silva’s Data Analysis, which seems really good, though I’m only at chapter 3. My only complaint is that I wish there were exercises at the end of each chapter.

[snarles]

Very nice. I would recommend it over Jaynes for anyone interested in learning what statistics is all about.