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.
- 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:
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.
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.
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been a huge need for a 'Jaynes-lite' which offers the philosophical grounding of P:tLoS sans its distracting (and now outdated) polemics.
How does this compare to Data Analysis: A Bayesian Tutorial? In any case, you should post your suggestion in the Best Textbooks thread.
I haven't looked through Silva. Kadane does have the advantage of being free to access, however!
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.
Very nice. I would recommend it over Jaynes for anyone interested in learning what statistics is all about.