Computation of the MLE for bivariate interval censored data

author: Marloes Maathuis, ETH Zurich

Description

I will discuss the new R-package 'MLEcens', which computes the nonparametric maximum likelihood estimator (MLE) for the distribution function of bivariate interval censored data. The computation of the MLE consists of two steps: a parameter reduction step and an optimization step. I will discuss algorithms for both steps. I will also illustrate the R-package using several examples.

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*Slides*
0:00	Computation of the MLE for bivariate interval censored data
0:05	Bivariate interval censored data: an example - 1
0:40	Bivariate interval censored data: an example - 2
0:51	Bivariate interval censored data: an example - 3
1:08	Bivariate interval censored data: an example - 4
1:12	Bivariate interval censored data: an example - 5
1:32	Bivariate interval censored data: an example - 6
1:43	Bivariate interval censored data: an example - 7
1:58	Bivariate interval censored data: an example - 8
2:34	The nonparametric maximum likelihood estimator - 1
2:44	- Questions
2:50	The nonparametric maximum likelihood estimator - 1
4:00	The nonparametric maximum likelihood estimator - 2
4:13	The nonparametric maximum likelihood estimator - 3
4:15	The nonparametric maximum likelihood estimator - 4
4:26	The nonparametric maximum likelihood estimator - 5
4:29	The nonparametric maximum likelihood estimator - 6
4:38	The nonparametric maximum likelihood estimator - 7
5:06	The nonparametric maximum likelihood estimator - 8
5:27	The nonparametric maximum likelihood estimator - 9
5:43	The nonparametric maximum likelihood estimator - 10
6:09	The nonparametric maximum likelihood estimator - 11
6:20	The nonparametric maximum likelihood estimator - 12
6:52	Difficulty in the computation of the MLE - 1
6:58	The nonparametric maximum likelihood estimator - 12
7:03	Difficulty in the computation of the MLE - 1
7:39	Difficulty in the computation of the MLE - 2
8:11	Outline
8:43	Reduction step - 1
10:06	The nonparametric maximum likelihood estimator - 12
10:24	Reduction step - 1
10:36	Reduction step - 2
11:10	Reduction step - 3
11:25	Height map algorithm - 1
12:27	Height map algorithm - 2
12:54	Height map algorithm - 3
13:09	The algorithm
13:35	Transform rectangles into canonical rectangles - 1
13:46	Transform rectangles into canonical rectangles - 2
13:51	Transform rectangles into canonical rectangles - 3
14:03	Transform rectangles into canonical rectangles - 4
14:06	Transform rectangles into canonical rectangles - 5
14:08	Transform rectangles into canonical rectangles - 6
14:13	Transform rectangles into canonical rectangles - 7
14:24	Transform rectangles into canonical rectangles - 8
14:35	Transform rectangles into canonical rectangles - 9
14:46	Transform rectangles into canonical rectangles - 10
14:52	Transform rectangles into canonical rectangles - 11
15:04	Transform rectangles into canonical rectangles - 12
15:22	Transform rectangles into canonical rectangles - 13
16:05	Why use canonical rectangles?
16:33	Transform rectangles into canonical rectangles - 13
16:41	Why use canonical rectangles?
16:43	Find local maxima by sweeping through the height map - 1
16:53	Find local maxima by sweeping through the height map - 2
17:11	Find local maxima by sweeping through the height map - 3
17:52	Find local maxima by sweeping through the height map - 4
18:08	Find local maxima by sweeping through the height map - 5
18:27	Find local maxima by sweeping through the height map - 6
18:37	Find local maxima by sweeping through the height map - 7
18:49	Find local maxima by sweeping through the height map - 8
18:52	Find local maxima by sweeping through the height map - 9
18:55	Find local maxima by sweeping through the height map - 10
19:11	Find local maxima by sweeping through the height map - 11
19:21	Find local maxima by sweeping through the height map - 12
19:37	Find local maxima by sweeping through the height map - 13
20:23	Find local maxima by sweeping through the height map - 14
20:34	- Questions
22:45	Find local maxima by sweeping through the height map - 15
22:54	Find local maxima by sweeping through the height map - 16
22:58	Find local maxima by sweeping through the height map - 17
23:00	Find local maxima by sweeping through the height map - 18
23:17	Find local maxima by sweeping through the height map - 19
23:19	Find local maxima by sweeping through the height map - 20
23:28	Find local maxima by sweeping through the height map - 21
23:29	Find local maxima by sweeping through the height map - 22
23:53	Find local maxima by sweeping through the height map - 23
24:00	Time and space complexity of the algorithm - 1
24:44	Time and space complexity of the algorithm - 2
25:19	Simulation study - 1
25:44	Simulation study - 2
25:59	Simulation study - 3
26:00	Simulation study - 4
26:02	Simulation study - 5
26:03	Simulation study - 6
26:08	Simulation study - 7
27:37	Computing the MLE: optimization step - 1
27:40	- Questions
28:01	- Questions
28:27	Computing the MLE: optimization step - 1
28:50	Computing the MLE: optimization step - 2
28:52	Computing the MLE: optimization step - 3
29:28	Computing the MLE: optimization step - 4
30:04	Computing the MLE: optimization step - 5
30:59	Necessary and sufficient conditions for the MLE - 1
31:13	Necessary and sufficient conditions for the MLE - 2
31:39	Necessary and sufficient conditions for the MLE - 3
31:46	Necessary and sufficient conditions for the MLE - 4
32:05	Necessary and sufficient conditions for the MLE - 5
32:19	Necessary and sufficient conditions for the MLE - 6
32:35	Necessary and sufficient conditions for the MLE - 7
32:53	Iterative algorithm for optimization step - 1
33:06	Iterative algorithm for optimization step - 2
33:18	Iterative algorithm for optimization step - 3
33:26	Iterative algorithm for optimization step - 4
33:35	Iterative algorithm for optimization step - 5
33:56	Iterative algorithm for optimization step - 6
34:20	Iterative algorithm for optimization step - 7
34:43	R-packages for interval censored data - 1
35:23	R-packages for interval censored data - 2
35:57	Structure of R-package - 1
36:12	Structure of R-package - 2
36:17	Structure of R-package - 3
36:35	Structure of R-package - 4
36:53	Structure of R-package - 5
37:10	Overview of MLEcens - 1
38:29	Overview of MLEcens - 2
39:05	Overview of MLEcens - 3
39:07	- Questions

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