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Let X; € {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2, ..., X, fxp(x | p) = (1 – p)*-"p for 0 < p <1 defined on r E {1,2,3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 3. Show that for n >> a + B, the posterior mean is approximately equal to the MLE. 4. Here is some data of sample size n = 30 х%3D с (11, 1, 17, 2, 2, 2, 1, 1, 6, 2, 1, 7, 2, 24, 5, 6, 4, 2, 10, 2, 1, 1, 5, 8, 4, 2, 1, 2, 4, 1) Using this data and p ~ Beta(10, 10) prior, find the posterior, posterior mean, and a 95% credible interval using the percentile approach. You can use R functions for calculations.

Let X; € {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2, ..., X, fxp(x | p) = (1 – p)*-"p for 0 < p <1 defined on r E {1,2,3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 3. Show that for n >> a + B, the posterior mean is approximately equal to the MLE. 4. Here is some data of sample size n = 30 х%3D с (11, 1, 17, 2, 2, 2, 1, 1, 6, 2, 1, 7, 2, 24, 5, 6, 4, 2, 10, 2, 1, 1, 5, 8, 4, 2, 1, 2, 4, 1) Using this data and p ~ Beta(10, 10) prior, find the posterior, posterior mean, and a 95% credible interval using the percentile approach. You can use R functions for calculations.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Answer parts 3 and 4 of the problem below.

Let X; E {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2,..., X, fxp(x | p) = (1 – p)*-'p for 0 < p< 1 defined on r E {1,2, 3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 3. Show that forn >> a + B, the posterior mean is approximately equal to the MLE. 4. Here is some data of sample size n = 30 х%3D с (11, 1, 17, 2, 2, 2, 1, 1, 6, 2, 1, 7, 2, 24, 5, 6, 4, 2, 10, 2, 1, 1, 5, 8, 4, 2, 1, 2, 4, 1) Using this data and p ~ Beta(10, 10) prior, find the posterior, posterior mean, and a 95% credible interval using the percentile approach. You can use R functions for calculations.
Transcribed Image Text:Let X; E {1,2, 3, ...} be the number of days until relapse for patient i who is diagnosed with multiple sclerosis and currently in remission. We model this data using a geometric distribution with pmf iid X1, X2,..., X, fxp(x | p) = (1 – p)*-'p for 0 < p< 1 defined on r E {1,2, 3, ...} and 0 elsewhere. Here, p is the risk of relapse on each day. 3. Show that forn >> a + B, the posterior mean is approximately equal to the MLE. 4. Here is some data of sample size n = 30 х%3D с (11, 1, 17, 2, 2, 2, 1, 1, 6, 2, 1, 7, 2, 24, 5, 6, 4, 2, 10, 2, 1, 1, 5, 8, 4, 2, 1, 2, 4, 1) Using this data and p ~ Beta(10, 10) prior, find the posterior, posterior mean, and a 95% credible interval using the percentile approach. You can use R functions for calculations.
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