Yes, that's exactly what the objective of this book is! I am not using computation out of necessity, but rather because I think it provides leverage for understanding the concepts, and learning to (as you say) compose traditional models and build new ones.

As the book comes along, I am finding that many ideas that are hard to explain and understand mathematically can be very easy to express computationally, especially using discrete approximations to continuous distributions.

For example, I just posted a section on ABC

http://www.greenteapress.com/thinkbayes/html/thinkbayes008.h...

that (I think) really demonstrates the strength of this approach.

Of course, my premise only applies for people who are as comfortable with programming as with math, or more so.

I'd recommend using as many real examples as possible. Things like forecasting, product recommendations, topic modeling, etc. While you can conceptually explain how Bayesian statistics is a unified recipe, it's incredibly hard to have this sink in with toy problems. This is especially true since many people using traditional tools are actually using advanced methods to solve real problems, so when they start reading about urns or doors it all comes across as rather academic. That's sad because the benefit of Bayesian coherency is mostly that it leads to a highly productive mode of practical data analysis.

Definitely shoot me an email at [email protected] if you're interested in the computational side of this area. At Sense (http://www.senseplatform.com), we're working on making applied Bayesian analysis as amazing as it should be.

E.T. Jaynes book, "Probability Theory: the Logic of Science" may come close to what you want. It emphasize that there are rules of thought, which lead to Bayesian statistics. As such, Bayesian statistics aren't just a recipe, but the law.

Now, I can only personally vouch for the first 2 chapters, as I haven't read the rest yet.

The greatness of this book cannot be overstated

Agree. It is unbelievable - one has to study it to believe it.

Going to Amazon right now...

* edit: Doh, no Kindle version. I don't mind paying $90+ for a good book though, just like it to be electronic: http://www.amazon.com/Probability-Theory-The-Logic-Science/d...

Free pdf is available here:

http://bayes.wustl.edu/etj/prob/book.pdf

It's always nice to see good things come out of Wash U. (Alum here.)

Unfortunately, it's only the first 95 pages.

There must be a fuller version floating around, though; my PDF version has 548 pages and ends with Appendix E, 'Multivariate Gaussian Integrals'.

EDIT: In case anyone wants to make me feel bad about pirating, Jaynes is dead, and besides that, I bought a hardcopy as backup.

I found the full text here:

http://www.naturalthinker.net/trl/texts/Science/Jaynes,%20E....

The first couple pages are a bit funny looking, but after that, there are all 500+ pages. It was the fourth result on Google for me.

Well, it's available on Google Books [1], but I don't know about $63 for what appears to be a skewed scan of the print book.

Personally, I searched out a PDF and based on what I've read so far, I'm itching to pull the trigger on Amazon as I'm simply loving what I'm reading.

1: http://goo.gl/UHMBi