Distant Kin in the EM Family

1. Distant Kin in the EM Family David A. van Dyk Department of Statistics University of California, Irvine . (Joint work with Xiao Li Meng and Taeyong Park.)

2. Outline The EM Family Tree The Stochastic Cousins Some Odd Relations Nested EM and The Partially Blocked Gibbs Sampler A Newly Found Kinsman A Stochastic ECME/AECM Sampler: The Partially Collapsed Gibbs Sampler

3. The EM Family Tree

4. Stochastic Cousins

5. The EM and DA Algorithms

6. An NEM Algorithm
with a Monte Carlo E-step

7. A Partially-Blocked Sampler

8. Ordering CM-steps in ECME

9. A Stochastic Version of ECME

10. AECM and Partially Collapsed Samplers

11. Completely Collapsed Samplers

12. Reducing Conditioning in Gibbs: The Simplest Example Consider a two-step Gibbs Sampler:

13. Heads Up!! Reducing the conditioning within Gibbs involves new challenges: The order of the draws may effect the stationary distribution of the chain. The conditional distributions may no be compatible with any joint distribution. The steps sometimes can be blocked to form an ordinary Gibbs sampler with fewer steps.

14. An Example from Astronomy Parameterized Latent Poisson Process Underlying Poisson intensity is a mixture of a broad feature and several narrow features. The �line location� and mixture indicator are highly correlated.

15. An Example from Astronomy Standard sampler simulates

16. An Incompatible Gibbs Sampler

17. Computational Gains

18. Verifying the Stationary Distribution of Sampler 2

19. The General Strategy