Principles of Uncertainty, Author Joseph Kadane (CRC Press)

http://www.crcpress.com/product/isbn/9781439861615

Watch Joseph Kadane, author of Principles of Uncertainty speak at the JSM2011.

Features

Well-written and comprehensive introduction to theory of Bayesian statistics
Each of the introductory chapters begins by introducing one new concept or assumption
Uses "just-in-time mathematics"—the introduction to mathematical ideas just before they are applied
Each chapter ends with a summary and exercises