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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Answer parts 3 and 4 of the problem below.
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman