Type I and type II errors for Multiple Simultaneous Hypothesis Testing

A set-output point of view on FDR control in multiple testing

author: Etienne Roquain, INRA - Paris

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*Slides*
0:00	A set-output point of view on FDR control
0:15	Outline
0:54	Outline01
1:06	General Setting of multiple testing
1:35	General Setting of multiple testing01
2:05	General Setting of multiple testing02
2:55	General Setting of multiple testing03
3:23	Type I error
3:32	Type I error01
3:55	Type I error02
4:47	Type I error03
5:37	Goal in FDR control
6:01	Goal in FDR control01
6:25	Goal in FDR control02
6:38	Part I - A set-output point of view on classical procedures
6:50	I.1. The \"cardinal control\" condition
7:05	I.1. The \"cardinal control\" condition01
7:17	I.1. The \"cardinal control\" condition02
8:08	I.1. The \"cardinal control\" condition03
8:39	I.1. The \"cardinal control\" condition (2)
10:16	I.1. The \"cardinal control\" condition (2)01
10:45	I.1. Condition () ) FDR control
11:46	I.1. Condition () ) FDR control01
12:28	I.1. Condition () ) FDR control02
13:11	I.1. Condition () ) FDR control03
13:22	I.1. Proof of Lemma 1
13:27	I.1. Proof of Lemma 1 01
13:38	I.1. Proof of Lemma 2
14:03	I.2. Step-up procedures satisfy ()
14:32	I.2. Step-up procedures satisfy () 01
15:16	I.2. Step-up procedures satisfy () 02
15:31	I.2. Using Lemma 1
15:56	I.2. Using Lemma 1 01
16:02	I.2. Using Lemma 1 02
16:17	I.2. Using Lemma 1 03
16:29	I.2. Using Lemma 1 04
16:54	I.2. Using Lemma 2
17:26	I.2. Using Lemma 2 01
17:31	I.2. Using Lemma 2 02
18:08	I.2. Using Lemma 2 03
18:58	I.2. Using Lemma 2 04
19:03	I.2. Threshold functions with Dirac prior
19:50	I.2. Threshold functions with Dirac prior 01
20:06	I.2. Threshold functions with power prior
20:23	I.2. Threshold functions with power prior 01
20:35	I.2. Threshold functions with power prior 02
21:27	I.2. Threshold functions with Gaussian prior
22:05	I.2. Open problems
22:12	I.2. Open problems 01
22:26	I.2. Open problems 02
22:45	I.2. Open problems 03
22:57	Part I I - New adaptive procedures
23:13	I I.1. 0-adaptive procedures
23:39	I I.1. 0-adaptive procedures 01
24:05	I I.1. 0-adaptive procedures 02
24:35	I I.1. 0-adaptive procedures 03
24:53	I I.1. 0-adaptive procedures 04
25:22	I I.1. 0-adaptive procedures 05
25:37	I I.1. 0-adaptive procedures 06
26:00	I I.1. Existing 0-adaptive procedures
26:19	I I.1. Existing 0-adaptive procedures 01
27:01	I I.1. Existing 0-adaptive procedures 02
27:47	I I.1. New 0-adaptive procedures
28:15	I I.1. New 0-adaptive procedures 01
28:27	I.1. New one-stage adaptive procedure
29:10	I.1. New one-stage adaptive procedure 01
29:27	I.1. New one-stage adaptive procedure 02
29:58	I I.1. New two-stages adaptive procedure
30:27	I I.1. New two-stages adaptive procedure 01
30:53	I I.1. New two-stages adaptive procedure 02
31:15	I I.1. Simulations
31:36	I I.1. Simulations 01
31:56	I I.1. Simulations 02
32:00	I I.1. Simulations 03
32:30	I I.1. Simulations, FDR, indep
33:23	I I.1. Simulations, FDR, indep 01
33:46	I I.1. Simulations, Power, indep
34:05	I I.1. Simulations, Power, indep 01
34:16	I I.1. Simulations, FDR, with corr
34:46	I I.1. Simulations, FDR, with corr 01
35:12	I I.2. Under general dependence
35:37	I I.2. Under general dependence 01
36:29	I I.2. New two-stages adaptive procedure
37:03	I I.2. New two-stages adaptive procedure 01
37:38	I I.2. New two-stages adaptive procedure 02
37:49	I I.2. New two-stages adaptive procedure 03
37:57	Conclusion
38:35	Future works
38:45	Future works 01
39:29	Future works 02
39:44	Thank you for your attention!

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