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.