Some Math Prerequistites I suggest

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BNP needs us to be very familiar with some graduate-level mathematics, especially probability theory and measure-based real analysis. I am also strengthening my math knowledge right now. I can share you some books I use and find really good.

• Point-Set Topology:
  • Topology, James R. Munkres, 2nd Edition (2000)
    • Reading Chapter 2-4 gives us good enough understandings on some topological notions used in analysis
• Real Analysis:
  • Real Analysis, H.L.Royden & P.M.Fitzpatrick, 4th Edition
• Functional Analysis:
  • Lecture Notes on Functional Analysis, Alberto Bressan;
  • Applied Analysis, John K. Hunter & B. Nachtergaele
• Probability Theory:
  • A Probability Path, Sidney I. Resnick
    • I personally think it is a great book for students first learning probability theory. This book is comprehensive and provides rigorous proofs in a understandable way. It is also the textbook for STATS 621 at UMich.
  • Probability: Theory and Examples, Rick Durrett, 5th Edition
• To be continued

Mastering knowledge in the books I list here only helps you feel a bit more comfortable while reading materials in Bayesian Nonparametrics. It doesn’t mean that you will easily understand BNP with these math tools. These math are necessary but far from sufficient. BNP is appealing and difficult… KEEP LEARNING

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