Type I and type II errors for Multiple Simultaneous Hypothesis Testing

Resambling-based confidence regions and multiple tests for a correlated random vector

author: Sylvain Arlot, Université Paris Sud

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*Slides*
0:00	Resampling-based confidence regions and multiple tests for a correlated random vector
0:59	Model
1:31	Model_1
1:44	Model_2
1:54	Model_3
2:56	Model_4
3:29	Model_5
3:42	Model_6
3:55	Example : (neuro)images
4:20	Example : (neuro)images_1
4:27	Example : (neuro)images_2
5:18	Example : (neuro)images_3
5:24	Example : (neuro)images_4
5:49	Example : simulation experiment
6:33	Example : simulation experiment_1
6:43	Example : simulation experiment_2
7:30	(Gt)t2T2 m with m = 128 : bandwith $ correlations
8:15	Multiple Simultaneous Hypothesis Testing
9:01	Multiple Simultaneous Hypothesis Testing_1
9:15	Multiple Simultaneous Hypothesis Testing_2
9:26	Multiple Simultaneous Hypothesis Testing_3
9:30	Multiple Simultaneous Hypothesis Testing_4
10:03	Thresholding
11:15	Thresholding_1
12:02	Bonferroni threshold
12:16	Bonferroni threshold_1
12:51	Bonferroni threshold_2
13:06	Bonferroni threshold_3
13:19	Ideal threshold
13:27	Ideal threshold_1
13:41	Ideal threshold_2
14:12	Goal
14:19	Goal_1
14:25	Goal_2
14:46	Goal_3
14:55	Outline
15:30	Resampling principle [Efron 1979 ; ...]
16:12	Resampling principle [Efron 1979 ; ...]_1
16:36	Resampling principle [Efron 1979 ; ...]_2
16:50	Resampling principle [Efron 1979 ; ...]_3
17:46	Examples of resampling weights
17:54	Examples of resampling weights_1
18:42	Examples of resampling weights_2
19:07	Examples of resampling weights_3
19:32	Examples of resampling weights_4
20:32	Quantile method
20:38	Quantile method_1
21:37	Quantile method_2
22:02	Concentration method
22:41	Concentration method_1
22:49	Concentration method_2
23:15	Concentration method_3
24:00	Results from empirical process theory
24:08	Results from empirical process theory_1
24:34	Results from empirical process theory_3
25:16	Classical procedures and existing results
25:41	Classical procedures and existing results_1
26:28	Classical procedures and existing results_2
26:49	Concentration method : three ideas
27:00	Concentration method : three ideas_1
27:22	Concentration method : three ideas_2
27:38	First result
29:23	Sketch of the proof
29:50	Sketch of the proof_1
30:00	Sketch of the proof_2
30:15	Remarks
30:54	Remarks_1
31:07	Remarks_2
31:53	Remarks_3
32:07	Remarks_4
32:39	Choice of the weights
32:46	Choice of the weights_1
32:55	Choice of the weights_2
33:32	Choice of the weights_3
33:49	Simulations : n = 1000, K = 16384, = 1
35:24	Second concentration threshold
35:48	Second concentration threshold_1
36:10	Simulations : n = 1000, K = 16384, = 1
36:38	Method
37:19	Theorem
39:23	Remarks
39:35	Remarks_1
40:08	Remarks_2
40:11	Remarks_3
41:40	Simulations : n = 1000, K = 16384, = 1
42:31	Simulations : without the additive term ?
43:43	Step-down procedure [Holm 1979 ; Westfall and Young 1993 ; Romano and Wolf 2005]
45:26	Step-down procedure
45:31	Step-down procedure_1
45:43	Step-down procedure_2
45:49	Step-down procedure_3
45:56	Step-down procedure_4
46:40	Simulations : with non-zero means, 0 μk 0.29, b = 24
47:54	Numerical simulation : 0 μk 0.29, b = 24
49:46	Conclusions
50:38	Conclusions_1
50:47	Conclusions_2
50:55	Conclusions_3
50:58	Conclusions_4
51:17	Future works
51:40	Future works_1
52:40	Future works_2
52:59	Thank you for your attention !

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