Nonparametric Bayesian Methods: Models, Algorithms, and Applications III

on YouTube ↗01h 02m

" summary

Shows how stick-breaking and the Polya/Chinese Restaurant logic arise from a Beta–Bernoulli De Finetti mix, then constructs completely random measures by placing a nonhomogeneous Poisson random measure on the product space (location × weight). Choosing the Lévy density alpha w^{-1} e^{-beta w} yields a gamma process with independent gamma marginals; normalizing those recovers the Dirichlet process. Uses the Levy–Khinchin theorem (Laplace functional) and moments; construction is explicit and rigorous.

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" chapters (8)

1. 0:00Random measures and stick breaking
2. 8:36Moments and stick breaking
3. 13:31Completely random measures
4. 22:56Poisson random measures
5. 31:13Gamma processes from CRMs
6. 44:51Gamma process marginals
7. 57:22Levy-Khinchin theorem
8. 1:00:13Summary and applications

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