I've recently started going through http://www.amazon.com/Data-Analysis-Bayesian-Devinderjit-Siv... and can highly recommend it. The benefits of Bayesian reasoning can be grasped somewhat easily without a detailed knowledge of the math, but at the end of the day scientists and engineers still need to learn how to use it and write programs using it to do stuff! One review mentions the book dives right into the subject, it does; I believe Bayes' Theorem is shown on page 6. Some people find a brisk pace hard to follow, personally I like it since I can always fill in the gaps with other material if needed. (Like Jaynes, or http://uncertainty.stat.cmu.edu/ )