Nonparametric Bayesian Methods: Models, Algorithms, and Applications II
summary
Covers how stick‑breaking GEM priors produce discrete random measures used as Dirichlet process priors, derives the Chinese restaurant and Pólya‑urn representations, and proves exchangeability via de Finetti so a hidden G generates IID draws; shows Gibbs/slice samplers and a sigma‑discount that yields Pitman‑Yor power‑laws and recovers K‑means in a zero‑noise limit. Expect concrete formulas (EPPF, alpha log N cluster growth), algorithm sketches for marginalization/augmentation, and pointers to Levy–Khintchine/Poisson calculus for deeper constructions.
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chapters (6)
- 0:00Introduction to nonparametric Bayes
- 14:49Dirichlet process as measure
- 24:04Chinese restaurant process
- 49:01De Finetti’s theorem
- 57:25Pitman-Yor process
- 1:03:04Summary and open directions
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