Exercises for Tue Feb 13_亚博娱乐官网_亚博pt手机客户端登录

nils
2018-02-09T16:07:42.106Z
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www.uio.no

1. On Feb 6 I went through more Dirichlet Process matters, including the Sethuranam stick-breaking representation, and how to simulate from a simple hierarchical setupt where parameters \theta_i stem from Dir(a P_0) and observattions are seen as y_i from f(y_i | x_i).

2. Check my R scripts com3a, com4a, com5a.

3. I also did a bit of Bayesian nonparametrics for the quantile function Q(y) = Finverse(y) = the minimum x for which F(x) \ge y. See also the Hjort-Petrone paper about such things which is now at the course webpage.

4. I'll rather soon tex up some Nils Exercises and Lecture Notes.

5. Exercises for Tue Feb 13:

(i) Use the stick-breaking representation to put an infinite sum representation for P(A), with A a fixed set. Show that E P(A) = p_0 = P_0(A), and find the 2nd and 3rd central means, E (P(A) - p_0)^2 and E (P(A) - p_0)^3. Check that these are as they should be, from the Beta distribution for P(A).

(ii) With n = 100 data poi...