1. Information geometry of Statistical inference with selective sample S. Eguchi, ISM & GUAS This talk is a part of co-work with J. Copas, University of Warwick

2. Local Sensitivity Approximation for Selectivity Bias. J. Copas and S. Eguchi J. Royal Statist. Soc. B, 63 (2001), 871-895. (http://www.ism.ac.jp/~eguchi/recent_preprint.html)

3. Summary

4. Statistical model Probability model

5. Near parametric exact parametric non-parametric near-parametric

6. Def. (X, Y, Z) is ignorable Ignorability

7. Observational status

8. Binary response with missing

9. Non-ignorable cases

10. Small degree of non-ignorability

11. Distributional expression

12. Tangent space and neighborhood

13. Exponential map

14. Tubular Neighborhood M

15. Decomposition

16. tangent and normal

17. Conditional Distribution

18. Calibration

19. Rosenbaum’s log odd ratio

20. Counterfactual

21. Guide line

22. Non-ignorable missing

23. Selectivity region

25. Unstable or Misspecifying

26. Regression formulation

27. Heckman model

28. Likelihood

29. Likelihood analysis where

30. Profile likelihood of 

31. N = 1435, n = 1323 

32. Skin cancer data

33. Various pattern of bias

34. Group comparison

35. Non-random allocation

36. Selection bias

37. Effect of sentence Z = 1 prison Z = 2 community service Z = 3 probation Y = ratio of reconviction Logistic model

38. Selectivity regions Probation effect Community service effect 01 ‐1‐1 ‐1‐1 1 0     C.I.

39. two-group comparison

40. Likelihood

41. Analysis

42. UK National Hearing Survey The effect of occupational noise Case (high level noise) Control Response Y is threshold of 3kHz sound

43. Case mean Control mean Pooled s. d. t-statistic Standard analysis supports high significance Conventional result

44. Non-random allocation

45. Future problem

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