Solved – Introductory textbook on nonparametric Bayesian models

Question

I'd like to wrap my head around this topic but learning from white-papers and tutorials is hard because there are many gaps which are usually filled in textbooks.

If it is important I have relatively strong mathematical background as I did my Ph.D. in applied mathematics (CFD to be more precise).

Answer 1

Regarding your comment to @jerad's solution, I believe that you don't have to get disappointed because you cannot prove formula 12. It needs some theory of Stochastic Processes. If you want to know how formula 12 is derived check at Ferguson's paper, A bayesian analysis of some nonparametric problems (The Annals of Statistics 1973, 1(2):209), who first proved the existence of Dirichlet Process and its properties.

In general, to study Bayesian Nonparametrics you need to study Probability Theory and Stochastic Processes. I mention down two books that are common in BNP are:

• Ghosh and Ramamoorthi, Bayesian Nonparametrics, Springer; 2003.
• Hjort, Holmes, Müller, and Walker, Bayesian Nonparametrics, Cambridge University Press; 2010.