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.
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.