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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 phd in applied mathematics (cfd to be more precise).

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As far as I know, no such book exists yet as the area is still quite new. The couple Bayesian nonparametrics books I've seen are basically just a bunch of review papers from various researchers bound together.

If you have a PhD in math, applied or not, I'm sure you can get your head around by reading the standard papers.

Probably the gentlest yet most thorough introduction to BNP methods is this tutorial by Sam Gershman.

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